Quiz 2

Question 1

Briefly describe two possible sources of confusion about the “average”

Answer 1

Two possible sources of confusion are not knowing whether the reported average is the mean or the median, and not having enough information about how the average was computed

Question 2

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false)
- A survey found that the mean salary for professional soccer players is much higher than the median salary

Answer 2

The statement makes sense, because it is likely that a few players have very high salaries, which are outliers and will pull the mean to a higher value than the median

Question 3

Determine whether the following statement makes sense (is clearly true) or does not make sense (is clearly false). Explain.
- A survey question asks respondents the number of car crashes they have been involved in during the past ten years.
- The sample of the results has modes of 0 and 1.

Answer 3

This statement makes sense because the mode is the most frequent value in a data set, and there may be more than one mode.

Question 4

Listed below are measurements of the “head injury criterion” for seven smalls cars tested in crashes by a traffic safety organization.
- Higher numbers are associated with a higher risk of injury.
- Find the mean, median, and mode of the listed numbers.
- Can you draw any conclusion about the risk of head injury in small cars versus larger cars?

512 542 468 379 489 478 509

Answer 4

The mean is 482.4
- The median is 489
- There is no mode
- None, because the data are all for small cars. They do not by themselves tell us anything about a comparison with larger cars.

The mean formula is mean = sum of all values divided by total number of values

The median is the middle value in the sorted data set (or halfway between the two middle values if the number of values is even)

The mode is the most common value (or group of values) in a data set. There is no mode if no value occurs more than once.

Question 5

Cans of soda vary slightly in weight.
- Given below are the measured weights of seven cans, in pounds.
- Find the mean and median of these weights.
- Which, if any, of these weights would be considered the outlier?
- What are the mean and median weights if the outlier is excluded?

0.8161 0.8194 0.8166 0.8172 0.7906 0.8142 0.8123

Answer 5

The mean is 0.81234
- The median is 0.8161
- The outlier is 0.7906
- The mean without the outlier is 0.81597
- The median without the outlier is 0.81635

An outlier in a data set is a value that is much higher or much lower than almost all other values

Question 6

Listed below are amounts (in millions of dollars) collected from parking meters by a security company in a certain city.
- A larger data set was used to convict 5 members of the company of grand larceny.
- Find the mean and median for each of the two samples and then compare the two sets of results.
- Do the limited data listed here show evidence of stealing by the security company’s employees?

Security company: 1.5 1.8 1.5 1.8 1.7 1.4 1.1 1.4 1.4 1.6

Other companies: 1.7 2.2 1.6 1.8 1.6 1.9 2.2 1.8 1.8 2.3

Answer 6

The mean for the security company is $1.52 million and the mean for the other companies is $1.89 million.
- The median for the security company is $1.5 million and the median for the other companies is $1.8 million.
- The mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies.
- Since the security company appears to have collected lower revenue than the other companies, there is some evidence of stealing by the security company’s employees.

Question 7

Distinguish between a uniform distribution and a distribution with one or more modes.
- What do we call a distribution with one, two, and three modes?

Answer 7

All data values in a uniform distribution have the same frequency, whereas a distribution with one or more modes has one or more values that occur most frequently.
- A distribution with one mode is called unimodal, a distribution with two modes is called bimodal, and a distribution with three modes is called trimodal.

Question 8

What is the difference between symmetry and skewness?

Answer 8

A distribution has skewness when it is lopsided, with values that are more spread out on either the right side or the left side.
- A distribution has symmetry when the left half is a mirror image of the right half.

Question 9

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false).
- Explain your reasoning.

• The distribution of grades was left skewed, but the mean, median, and mode were all the same.

Answer 9

This does not make sense because the mean and median should lie somewhere to the left of the mode for most left skewed distributions.

Question 10

In a recent year, the 870 players in a certain sports league had salaries with the characteristics below.
- The mean was $3,152,075.
- The median was $1,525,000.
- The salaries ranged from a low of $503,000 to a high of $28,000,000.

Answer 10

1. Describe the shape of the distribution of salaries. Is the distribution symmetric? Is it left skewed? Is it right skewed?
   - The distribution is right skewed.
2. About how many players had salaries of $1,525,000 or higher?
   - About 435 players had salaries of $1,525,000 or higher.

Question 11

For the distribution described below, complete parts a and b below.

The annual incomes of all those in a statistics class, including the instructor.

Answer 11

1. How many modes are expected for the distribution?
   - The distribution is probably unimodal.
2. Is the distribution expected to be symmetric, left skewed, or right skewed?
   - The distribution is probably right skewed.

Question 12

Consider two grocery stores at which the mean time in line is the same but the variation is different.
- At which store would you expect the customers to have more complaints about the waiting time?
- Explain.

Answer 12

The customers would have more complaints about the waiting time at the store that has more variation because some customers would have longer waits and might think they are being treated unequally.

Question 13

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false).
- Explain your reasoning.

The standard deviation for the heights of a group of 5 year old children is smaller than the standard deviation for the heights of a group of children who range in age from 3 to 15.

Answer 13

The statement makes sense because the range of data for the heights of a group of 5 year old children is smaller than the range of data for the heights of a group of children who range in age from 3 to 15.

Question 14

The celebrities with the top eight net worths (in millions of dollars) in a certain country in a recent year are shown in the table.
- Find the range and standard deviation of these data.
- If you considered all celebrities rather than just this group, would you expect these measures of variation in net worth to be larger, smaller, or the same?
Celebrity 1 = 5300
Celebrity 2 = 3800
Celebrity 3 = 3200
Celebrity 4 = 1900
Celebrity 5 = 1100
Celebrity 6 = 800
Celebrity 7 = 800
Celebrity 8 = 650

Answer 14

The range = 4650 million dollars
- The standard deviation for= 1723.5 million dollars
- If you considered all celebrities rather than just this group, these measures of variation in net worth would be larger.

The range of a set of data values is the difference between its highest and lowest data values.
Range = highest value (max) - lowest value (minimum)

The standard deviation is a measure of how widely data values are spread around the mean of a data set.
S = square root of E symbol times x - x to the -2 power divided by n-1.

Question 15

Ayurveda is a traditional medical system commonly used in India.
- Listed are the lead concentrations measured in different Ayurveda medicines (manufactured in the United States).
- Find the range and standard deviation of these data.
- Given that lead is considered a poison when it enters your bloodstream, what does the variation tell you about the safety of these traditional medicines?

2.9 6.3 5.1 5.9 20.9 7.6 11.8 20.8 11.1 17.3

Answer 15

The range is 18.
- The standard deviation is 6.62
- Lead is considered a poison when it enters your bloodstream. What does the variation in the data set tell you about the safety of these traditional medicines?
- The large variation suggests that you should be careful using these medicines, especially those with high lead values.

Question 16

Listed are measurements of blood alcohol concentration (BAC) of drivers who were involved in fatal crashes and then given jail sentences.
- Find the range and standard deviation of the data.
- Briefly comment on what the results mean in this case.
0.25 0.17 0.17 0.15 0.13 0.24 0.32 0.24 0.14 0.15 0.12 0.15

Answer 16

The range = 0.2
- The standard deviation = 0.062
- While some drunk drivers who caused fatalities had very high BAC levels, others were fairly close to the legal intoxication limit of 0.08. Given the small sample size, this suggests that even lower BAC levels could potentially be dangerous.

Question 17

One of the authors with too much time on his hands weighed each chocolate candy in a bag of 466 plain chocolate candies.

Answer 17

1. One of the chocolate candies weighed 0.776 gram and it was heavier than 24 of the other chocolate candies. What is the percentile of this particular value?
   - It is in the 5th percentile.
2. One of the chocolate candies weighed 0.876 gram and it was heavier than 328 of the other chocolate candies. What is the percentile of this particular value?
   - It is in the 70th percentile.
3. One of the chocolate candies weighed 0.856 gram and it was heavier than 221 of the other chocolate candies. What is the percentile of this particular value?
   - It is in the 47th percentile.

Percentile of data value = number of values less than this data value divided by total number of values in this data set multiplied by 100.

Question 18

A data set consists of the 80 ages of women at the time that they won an award in the category of best actress.

Answer 18

1. One of the actresses was 40 years of age, and she was older than 57 of the other actresses at the time that they won awards. What is the percentile of the age of 40?
   - 71st percentile.
2. One of the actresses was 54 years of age, and she was older than 72 of the other actresses at the time that they won awards. What is the percentile of the age of 54?
   - 90th percentile.
3. One of the actresses was 60 years of age, and she was older than 73 of the other actresses at the time that they won awards. What is the percentile of the age of 60?
   - 91st percentile.

Question 19

The following four sets of seven numbers all have a mean of 9.

(9,9,9,9,9,9,9), (7,7,9,9,9,11,11), (7,7,7,9,11,11,11), (4,4,4,9,14,14,14)

Answer 19

1. Construct a histogram for set (9,9,9,9,9,9). Choose the correct graph.
   - Answer is A.
2. Construct a histogram for set (7,7,9,9,9,11,11). Choose the correct graph.
   - Answer is C.
3. Construct a histogram for set (7,7,7,9,11,11,11). Choose the correct graph.
   - Answer is D.
4. Construct a histogram for set (4,4,4,9,14,14,14). Choose the correct graph.
   - Answer is D.
5. Give the five number summary and draw a box plot for each set. Give the five number summary for (9,9,9,9,9,9,9).
   - Low value = 9.
   - Lower quartile = 9.
   - Median = 9.
   - Upper quartile = 9.
   - High value = 9.
   - Answer for boxplot is C.
6. Give the five number summary for set (7,7,9,9,9,11,11).
   - Low value = 7.
   - Lower quartile = 7.
   - Median = 9.
   - Upper quartile = 11.
   - High value = 11.
   - Answer for boxplot is D.
7. Give the five number summary for set (7,7,7,9,11,11).
   - Low value = 7.
   - Lower quartile = 7.
   - Median = 9.
   - Upper quartile = 11.
   - High value = 11.
   - Boxplot answer is A.
8. Give the five number summary for set (4,4,4,9,14,14,14).
   - Low value = 4.
   - Lower quartile = 4.
   - Median = 9.
   - Upper quartile = 14.
   - High value = 14.
   - Boxplot answer is A.
9. Compute the standard deviation for each set. Compute the standard deviation for set (9,9,9,9,9,9,9).
   - S = 0.0
10. Compute the standard deviation for set (7,7,9,9,9,11,11).
    - S = 1.6
11. Compute the standard deviation for set (7,7,7,9,11,11,11).
    - S = 2.0
12. Compute the standard deviation for set (4,4,4,9,14,14,14).
    - S = 5.0
13. Based on your results, briefly explain how the standard deviation provides a useful single number summary of the variation in these data sets.
    - The standard deviation is a measure of how widely data values are spread around the mean of a data set.
    - Note that in the first data set, the difference between the highest and lowest values is zero and the standard deviation is 0.0, and in the last data set, the difference between the highest and lowest values is higher than in the other data sets and the standard deviation is the highest.

Question 20

A report claims that the returns for the investment portfolios with a single stock have a standard deviation of 0.57, while the returns for portfolios with 32 stocks have a standard deviation of 0.322.
- Explain how the standard deviation measures the risk in these two types of portfolios.

Answer 20

A lower standard deviation means more certainty in the return and less risk.
- Hence, the returns for portfolios with 32 stocks have less risk than the ones with a single stock.

Question 21

When referring to a “normal” distribution, does the word normal have the same meaning as it does in ordinary usage?
- Explain.

Answer 21

The word normal has a special meaning in statistics.
- It refers to a specific category of distributions that are symmetric and bell shaped with a single peak.
- The peak corresponds to the mean, median, and mode of such a distribution.

Question 22

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false).
- The explanation is more important than the answer.

Among a sample of 1044 adult women, pulse rates are normally distributed with a mean of 75.5 beats per minute, but 80% of the women have pulse rates greater than 75.5 beats per minute.

Answer 22

The statement does not make sense.
- For a normal distribution, only half of the women should have pulse rates above the mean.

Question 23

Consider the following three distributions.

Answer 23

1. Which distribution is not normal?
   - B.
2. Of the two normal distributions, which has the larger standard deviation?
   - C.

Question 24

Determine whether the following data set is likely to be normally distributed.
- Explain the reasoning.

The amounts of rainfall (in inches) on each day of a year in New York.

Answer 24

The given data set is not likely to be normally distributed.
- There will be many days with 0 inches of rain and very few days with large amounts of rain.
- There will be a peak in the distribution at the extreme left.

Question 25

Determine whether the following data set is likely to be normally distributed. - Explain the reasoning. The pulse rates of randomly selected adult females.

Answer 25

The given data set is likely to be normally distributed. - The pulse rates vary above and amounts. - The distribution has one peak and is symmetric. - Pulse rates result from a combination of many factors.

Question 26

The figure to the right shows a histogram for the body temperatures (Fahrenheit) of a sample of 505 adults. - Is this distribution close to normal? - For the population of all adults, should body temperature have a normal distribution? - Why or why not?

Answer 26

1. Is the distribution close to normal? - The histogram is symmetric around a single peak and bell shaped, so the distribution is close to normal. 2. For the population of all adults, should body temperature have a normal distribution? Why or why not? - Yes, because body temperature is a human trait determined by many genetic and environmental factors. The values for this variable should cluster near a mean and become less common farther from the mean, giving the distribution a bell shape.

Question 27

Consider the graph of a normal distribution which gives relative frequencies in a distribution of men’s heights. - The distribution has a mean of approximately 68 inches and a standard deviation of approximately 2 inches.

Answer 27

1. What is the total area under the curve? - The total area under the curve is 1.00 2. Estimate (using area) the relative frequency of values less than 66 inches. - 0.16 3. Estimate the relative frequency of values greater than 66 inches. - 0.84 4. Estimate the relative frequency of values between 66 and 68 inches. - 0.34 5. Estimate the relative frequency of values greater than 68 inches. - 0.50 - The area that lies under the normal distribution curve corresponding to a range of values on the horizontal axis is the relative frequency of those values. - To find the relative frequency of values less than 71, estimate the area under the curve to the left of 71. - To find the relative frequency of values greater than 71, estimate the area under the curve to the right of 71. - Recall that the sum of the areas to the left and to the right of some value must give the whole area under the curve. - To find the relative frequency of values between 71 and 74, estimate the area under the curve between 71 and 74. This area is equal to the difference between the areas to the left of 74 and 71. - Recall that the area under the curve to the left of 71 is 0.16. The area under the curve between 71 and 74 is 0.50 - 0.16 =0.34 - To find the relative frequency of values greater than 74, estimate the area under the curve to the right of 74. - Recall that the sum of the areas to the left and to the right of some value must give the whole area under the curve. The area under the curve to the right of 74 is 1 - 0.50 =0.5

Question 28

What is a standard score? - How do you find the standard score for a particular data value?

Answer 28

1. Choose the correct definition of a standard score. - A standard score is the number of standard deviations a data value lies above or below the mean. 2. Choose the correct formula for computing a standard score. - The standard score for a particular data value is given by z = data value - mean divided by standard deviation.

Question 29

Decide whether the following statement makes sense or does not make sense. - Explain your reasoning. My professor graded the final score on a curve, and she gave a grade of A to anyone who had a standard score of 2 or more.

Answer 29

This makes sense because a standard score of 2 or more corresponds to roughly the 97th percentile. - Though this curve is stingy on giving out A’s to students, it is still giving the top students the highest grade.

Question 30

A test of depth perception is designed so that scores are normally distributed with a mean of 47 and a standard deviation of 8. - Use the 68-95-99.7 rule.

Answer 30

1. Find the percentage of scores less than 47. - 50% 2. Find the percentage of scores less than 55. - 84.0% 3. Find the percentage of scores greater than 63. - 2.5% 4. Find the percentage of scores greater than 39. - 84.0% 5. Find the percentage of scores between 39 and 63. - 81.5% The normal distribution curve is symmetric. The total area under the curve is 1. A score of 52 is the mean so the percentage of scores less than 52 is 50%. - A score of 62 is 10 points, or 1 standard deviation, above the mean of 52. The rule states that about 68% of the scores are within 1 standard deviation of the mean. - Find the percentage of scores that are more than 1 standard deviation from the mean: 100% - 68% =32% - Half of this 32% of the scores are more than 1 standard deviation below the mean, and the other half of the scores are more than 1 standard deviation above the mean. So the percentage of scores greater than 62 is 16%. - Thus, the percentage of scores less than 62 is 100% - 16% =84%. - A score of 72 is 20 points, or 2 standard deviations, above the mean of 52. The rule states that about 95% of the scores are within 2 standard deviations of the mean. - Find the percentage of scores that are more than 2 standard deviations from the mean: 100% - 95% =5% - Half of this 5% of the scores are more than 2 standard deviations below the mean, and the other half of the scores are more than 2 standard deviations above the mean. So the percentage of scores greater than 72 is 2.5% - A score of 42 is 10 points, or 1 standard deviation, below the mean of 52. - Recall that half of 32% of the scores are more than 1 standard deviation below the mean, and the other half of the scores are more than 1 standard deviation above the mean. So the percentage of scores less than 42 is 16%. - Thus, find the percentage of scores greater than 42: 100% - 16% =84%. - A score of 42 is 10 points, or 1 standard deviation, below the mean of 52. The rule states that about 68% of the scores are within 1 standard deviation of the mean. - Half of this 68% of the scores are between the mean and 1 standard deviation below the mean. The percentage of scores between 42 and 52 is 34%. - Note that a score of 72 is 2 standard deviations above the mean of 52, so half of 95% of the scores are between the mean and 2 standard deviations above the mean. The percentage of scores between 52 and 72 is 47.5% - Thus, find the percentage of scores between 42 and 72: 34% + 47.5% =81.5%

Question 31

In a study of facial behavior, people in a control group are timed for eye contact in a 5 minute period. - Their times are normally distributed with a mean of 178.0 seconds and a standard deviation of 57.0 seconds. - Use the 68-95-99.7 rule to find the indicated quantity.

Answer 31

1. Find the percentage of times within 57.0 seconds of the mean of 178.0 seconds. - 68% 2. Find the percentage of times within 114.0 seconds of the mean of 178.0 seconds. - 95% 3. Find the percentage of times within 171.0 seconds of the mean of 178.0 seconds. - 99.7% 4. Find the percentage of times between 178.0 seconds and 292 seconds. - 47.5%

Question 32

Sketch the normal distribution of IQ scores, which has a mean of 100 and a standard deviation of 15, and then shade the described area. Use the accompanying table to find the percentage of scores greater than 104.

Answer 32

1. Sketch the normal distribution of scores and shade the described area. - The answer is graph C. 2. The percentage of scores greater than 104 - 39.49%

Question 33

Sketch the normal distribution of IQ scores, which has a mean of 100 and a standard deviation of 15, and then shade the described area. - Use the accompanying table to find the percentage of scores greater than 78.

Answer 33

1. The graph answer is C. 2. The percentage of scores greater than 78 is 92.88%

Question 34

Sketch the normal distribution of heights of adult males, which has a mean of 174 cm and a standard deviation of 7 cm, and then shade the described area. - Use the accompanying table to find the percentage of heights greater than 166 cm.

Answer 34

1. The graph is answer B. 2. The percentage of heights greater than 166 centimeters is 87.35%

Question 35

Sketch the normal distribution of heights of adult males, which has a mean of 174 m and a standard deviation of 7 cm, and then shade the described area. - Use the accompanying table to find the percentage of heights less than 145 cm.

Answer 35

1. The graph answer is A. 2. The percentage of heights less than 145 cm is 0.00%

Question 36

Large samples of the same size are randomly selected from a very large population that may or may not have a normal distribution. - What does the Central Limit Theorem tell us about the distribution of the means from those samples?

Answer 36

The means of the samples will have a distribution that is approximately a normal distribution.

Question 37

What is the Central Limit Theorem? - When does it apply?

Answer 37

1. Suppose that many random samples of size n for a variable are taken and the distribution of means of each sample is recorded. - The standard deviation of the distribution of means approaches 0 divided by the square root of n, where 0 is the standard deviation of the population. - The distribution of means will be approximately a normal distribution. - The mean of the distribution of means approaches the population mean, u. 2. When does the Central Limit Theorem appply? - The Central Limit Theorem applies to variables with any distribution (not necessarily a normal distribution). - The Central Limit Theorem applies for suitably large sample sizes. A common threshold is n > 30.

Question 38

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). - Explain clearly. A process consists of repeating this operation: Randomly selected two values from a normally distributed population and then find the mean of the two values. The sample means will be normally distributed, even though each sample has only two values.

Answer 38

The statement makes sense. - Since the population is normally distributed, the distribution of sample means will also be normally distributed, regardless of sample size.

Question 39

IQ scores are normally distributed with a mean of 105 and a standard deviation of 15. - Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.

Answer 39

1. If the sample size is n = 81, find the mean and standard deviation of the distribution of sample means. - The mean of the distribution of sample means is 105. - The standard deviation of the distribution of sample means is 1.7 2. If the sample size is n = 169, find the mean and standard deviation of the distribution of sample means. - The mean of the distribution of sample means is 105. - The standard deviation of the distribution of sample means is 1.2 3. Why is the standard deviation in part a different from the standard deviation in part b? - With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation. - The standard deviation is 0 divided by the square root of n where 0 is the standard deviation of the population.

Question 40

Rolling a fair ten sided die produces a uniformly distributed set of numbers between 1 and 10 with a mean of 5.5 and a standard deviation of 2.872. - Assume that n ten sided dice are rolled many times and the mean of the n outcomes is computed each time.

Answer 40

1. Find the mean and the standard deviation of the resulting distribution of sample means for n = 144. - The mean of the resulting distribution of sample means is 5.5 - The standard deviation of the distribution of sample means is 0.239 2. Find the mean and the standard deviation of the resulting distribution of sample means for n = 36. - The mean of the resulting distribution of sample means is 5.5 - The standard deviation of the distribution of sample means is 0.479 3. Why is the standard deviation in part a different from the standard deviation in part b? - With larger sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

Question 41

Suppose you toss a coin 100 times. - Should you expect to get exactly 50 heads? - Why or why not?

Answer 41

No, there will be small deviations by chance, but if the coin is fair, the result should be close to 50 heads.

Question 42

Does the idea of statistical significance apply to samples or populations? - Briefly explain why.

Answer 42

Statistical significance applies to samples because the values of population parameters have no uncertainty.

Question 43

State whether the difference between what occurred and what you would have expected by chance is statistically significant. - Discuss any implications of the statistical significance. Nearly all of the passengers of an aircraft that is nearly full, with 90 passengers, are adult females.

Answer 43

The difference is statistically significant, since the probability of having that many passengers of one sex is less than 0.05. - This result suggests that this is not a normal flight.

Question 44

One experiment conducted a clinical trial of a method for gender selection. - According to this experiment, 350 babies had been born to parents using the new method to increase the probability of conceiving a girl, and 327 of those babies were girls. - Discuss whether these results appear to be statistically significant.

Answer 44

Yes.

Question 45

In a study by researchers, the body temperatures of 120 individuals were measured; the mean for the sample was 97.49 degrees Fahrenheit. - It is commonly believed that the mean body temperature is 98.60 degrees Fahrenheit. - The difference between the sample mean and the accepted value is significant at the 0.05 level.

Answer 45

1. Discuss the meaning of the significance level in this case. - If 100 samples were selected, the mean temperature would be 97.49 degrees Fahrenheit or less in 5 or fewer of the samples. 2. If we assume that the mean body temperature is actually 98.6 degrees Fahrenheit, the probability of getting a sample with a mean of 97.49 degrees Fahrenheit or less is 0.000000001. Interpret this probability value. - Selecting a sample with a mean this small is extremely unlikely and would not be expected by chance.

Question 46

Briefly describe the differences among theoretical, relative frequency, and subjective techniques for finding probabilities. - Give an example of each.

Answer 46

1. What are the differences among theoretical, relative frequency, and subjective techniques for finding probabilities? - The theoretical technique is based on the assumption that all outcomes are equally likely, while the relative frequency technique is based on observations or experiments, and the subjective technique is an estimate based on experience or intuition. 2. Which one of the following is an example of a theoretical probability? - The probability of rolling a 3 on a single die is 1 in 6. 3. Which of the following is an example of a relative frequency probability? - Based on statistical data, the chance of having the championship team coming from the Eastern Conference of a certain basketball league is about 1 in 10. 4. Which one of the following is an example of a subjective probability? - My teacher assures me that he is certain that my SAT scores will be the highest for the entire country.

Question 47

Determine whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). - Explain clearly. I estimate that there is a probability of 0.5 that a paper will be assigned in one of my classes sometime within the next 7 days.

Answer 47

The statement makes sense. - A subjective probability can be based on intuition, and it is reasonable to think that there is a 50% chance of the event described occurring.

Question 48

How many different arrangements of males and females are possible in three child families if birth order is taken into account? - What is the probability of a three child family with exactly three males? - Assume that none of the children are intersex.

Answer 48

There are 8 different three child families possible if birth order is taken into account. - There is a 1 in 8 probability of a three child family with exactly three males.

Question 49

Use the theoretical method to determine the probability of the following outcome and event. - State any assumptions made. Tossing two coins and getting either one head or two heads.

Answer 49

Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 3 in 4.

Question 50

An experiment consists of drawing 1 card from a standard 52 card deck. - What is the probability of drawing a 2?

Answer 50

The probability of drawing a 2 is 1 in 13. - Count the total number of possible outcomes. Among all the possible outcomes, count the number of ways the event of interest can occur. Determine the probability using this formula: Probability = the number of ways A can occur divided by the total number of possible outcomes. Then simplify.

Question 51

Use the theoretical method to determine the probability of finding that the next person you meet has the same birthday as yours (ignoring leap years). - State any assumptions that you need to make.

Answer 51

The probability is 1 in 365, assuming that the next person you meet is equally likely to have any possible birthday (excluding leap years).

Question 52

Determine the probability of the given complementary event. What is the probability that a 49% free throw shooter will miss her next free throw?

Answer 52

The probability that a 49% free throw shooter will miss her next free throw is 0.51

Question 53

Use the theoretical method to determine the probability of a given outcome or event. A bag contains 5 red candies, 10 blue candies, and 15 yellow candies. - What is the probability of drawing a red candy? A blue candy? A yellow candy? Something besides a yellow candy?

Answer 53

- The probability of drawing a red candy is 0.17 - The probability of drawing a blue candy is 0.33 - The probability of drawing a yellow candy is 0.5 - The probability of drawing something besides a yellow candy is 0.5

Question 54

What is the law of large numbers? - Can it be applied to a single observation or experiment? - Explain.

Answer 54

1. The law of large numbers states that if a process is repeated through many trials, the proportion of the trials in which event A occurs will be close to the probability P(A). 2. It does not apply to a single trial (observation or experiment), or even to small numbers of trials, but only to a large number of trials.

Question 55

What is the gambler’s fallacy? - Give an example.

Answer 55

1. The gambler’s fallacy is believing that a streak of bad luck makes a person due for a streak of good luck (or that a streak of good luck will continue). 2. There is a game where a person can bet $1 to decide if the next card on top of a standard deck will be red or black. - The person plays 100 games, choosing red every time and loses 55. - The person believes they will win if they play another 100 games.

Question 56

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). - Explain your reasoning. I haven’t won in my last 25 pulls on the slot machine, so I’m due to win on the next pull.

Answer 56

The statement does not make sense. - This represents the gambler’s fallacy.

Question 57

Suppose a man who has a habit of driving fast has never had a speeding ticket. - What does it mean to say that the law of averages (large numbers) will catch up with him? - Is it true? - Explain.

Answer 57

It means the person is “due” for a speeding ticket. - If tickets are given to speeding drivers at random, it is not true, because the probability that he gets a ticket when he next drives is not affected by what has happened on past drives.

Question 58

If you bet $10 in a pick 4 lottery game, you either lose $10 or gain $3,990. - (The winning prize is $4,000, but your $10 bet is not returned, so the net gain is $3,990). - The game is played by selecting a four digit number between 0000 and 9999, inclusive. - What is the probability of winning? - If you bet $10 on 1234, what is the expected value of your gain or loss?

Answer 58

1. 1 in 10,000 is the probability of winning. 2. The expected value of betting $10 on 1234 is -$9.60 The expected value of a variable is the weighted average of all its possible values. - Consider two events, each with its own value and probability. - The expected value formula is: Expected value = value of event 1 x probability of event 1 + value of event 2 x probability of event 2

Question 59

Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. - The bus arrives regularly every 100 minutes without delay. - What is the expected value of your waiting time?

Answer 59

The expected value of the waiting time is 50 minutes.

Question 60

When you give $5 for a bet in a casino game, there is a 252/495 probability that you will lose $5 and there is a 243/495 probability that you will make a net gain of $5. - (If you win, the casino gives you $5 and you get to keep your $5 bet, so the net gain is $5.) - What is the expected value? - In the long run, how much do you lose for each dollar bet?

Answer 60

The expected value is -9.09 cents. You lose 1.8 cents in the long run for each bet.

Question 61

Sports league players question got fucked up. How to calculate salaries is needed.

Question 62

Normal distribution of IQs question was fucked up as well. Both answers were wrong. Figure that shit out.