Midterm

Question 1

The median and mode of a normal distribution is equal to the mean (μ).

Answer 1

True

Question 2

In a normal probability distribution, the probability of having a value greater than the mean, written as P(X > μ), is equal to 0.5000.

Answer 2

True

Question 3

The standard normal distribution is a specific instance of the normal distribution with a mean (μ) of 1 and a standard deviation (σ) of 1.

Answer 3

False

Question 4

The normal distribution is symmetrical around its mean, μ.

Answer 4

True

Question 5

In a normal distribution, the standard deviation (σ) and the mean (μ) are always equal to each other.

Answer 5

False

Question 6

In a normal probability distribution, the probability of having a value less than the one standard deviation below the mean, written as P(X < μ - σ), is equal to 0.1587.

Answer 6

True

Question 7

After taking a statistics exam, a student is told that their exam had a z-score of -1.0. The instructor states that the exam scores follow a normal distribution with a mean (μ) of 75 and a standard deviation (σ) of 10. That is, if X is a random variable representing a score from the exam, then X ~ N(75, 102).

Answer 7

• The student’s score on the exam was 65.
• The student’s score on the exam was 1.0 standard deviation below the average score on the exam.

Question 8

For a value x taken from a normal distribution with a known mean μ and known standard deviation σ, what formula would you use to calculate the associated z-score?

Answer 8

z = x - μ / σ

Question 9

Approximately what proportion in a normal distribution will be within two standard deviations (σ) of the mean (μ)?

Answer 9

0.955, or 95.5%

Question 10

Of the four normal distributions illustrated here, which one has the largest variance?

Answer 10

Curve A (the flattest one)

Question 11

The Blue Ridge Caravan Company runs a regular shipping route from Charleston, WV to Arlington, WV. The number of hours that the route takes follows a normal distribution with a mean (μ) of 2.67 hours and a standard deviation (σ) of 0.22 hours. What is the z-score for a shipping route that takes 3.27 hours?

Answer 11

2.73

Question 12

A study suggests that the daily average time that an 18-year old spends playing video games has a normal distribution with a mean (μ) of 2.5 hours and a standard deviation (σ) of 0.7 hours. An 18-year old, selected at random, tells you that the spend 2.6 hours per day, on average, playing video games. What is z-score corresponding to 2.6 hours per day?

Answer 12

0.14

Question 13

For a normal distribution with mean μ and standard deviation σ, what is the probability of an observation greater than one standard deviation above the mean (shown below)?

Answer 13

0.1587

Question 14

Corley Motors, a manufacturer of fine motorcycles, has a factory that assembles motorcycles to be delivered to dealerships for sale. The mean (μ) length of time for the assembly process for their flagship motorcycle is 76.5 minutes with a standard deviation (σ) of 7.3 minutes. A motorcycle is assembled and takes 79.9 minutes. What is the z-score corresponding to 79.9 minutes?

Answer 14

0.47

Question 15

At the Slocum’s Joe chain of coffee and donut shops, the automated coffee machine fills 16oz coffee cups with an amount of coffee that follows a normal distribution with a mean (μ) of 15.80oz and a standard deviation (σ) of 0.12oz. The cup used for a 16oz coffee can only hold 16.10oz, at which point it overflows. What is the probability that the automated coffee machine fills a 16oz coffee past 16.10oz (thus, overflowing the cup)?

Answer 15

0.0062

Question 16

For a normal distribution with mean μ and standard deviation σ, what is the probability of an observation between -1.5σ and 0.5σ (shown below)?

Answer 16

0.6247

Question 17

Umbrella Pharmaceuticals is developing various new retro-viral therapies based on recent viral research. One of their test therapies, labeled Sample G, has a mean (μ) retro-viral doubling time of 155 seconds with a standard deviation (σ) of 20 seconds. Unfortunately, if the retro-viral doubling time of the sample is less than 110 seconds, it is deemed “out of control” and the sample has to be terminated. What is the probability that a test sample is deemed “out of control” and has to be terminated?

Answer 17

0.0122

Question 18

For a normal distribution with mean μ = 0 and standard deviation σ = 1, what is the z-score corresponding to a lower-tail probability of .0500 (shown below)?

Answer 18

1.65

Question 19

The standard normal distribution is a specific instance of the normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1.

Answer 19

True

Question 20

In a normal probability distribution, the probability of having a value less than the one standard deviation below the mean, written as P(X < μ - σ), is equal to 0.8413.

Answer 20

False

Question 21

The standard deviation of the sampling distribution (sometimes known as the Standard Error) is equal to the standard deviation of the population distribution divided by the square root of the sample size.

Answer 21

True

Question 22

The shape of the sampling distribution is the same shape as the distribution of the population from which the was taken.

Answer 22

False

Question 23

In a normal probability distribution, the probability of having a value between the mean and one standard deviation above the mean, written as P(μ < X < μ + σ), is equal to 0.3413.

Answer 23

True

Question 24

When taking a sample from a population, a larger sample size will result in a larger variance of the sampling distribution.

Answer 24

False

Question 25

Andrew's doctor told him that the z-score for his systolic blood pressure is 1.5. Assume that the systolic blood pressure (given in millimeters of mercury, or mmHg) of males follows a normal distribution with a mean (μ) of 125 and a standard deviation (σ) of 14. That is, if X is a random variable representing a male systolic blood pressure score, then X ~ N(125, 142).

Answer 25

- Andrew's systolic blood pressure is 1.5 standard deviations above the average blood pressure of men. - Andrew's systolic blood pressure is 146 mmHg.

Question 26

When taking a sample of size n from a population with mean μ and standard deviation σ, what is the mean of the corresponding sampling distribution (μx̄)?

Answer 26

The population mean (μ)

Question 27

Approximately what proportion in a normal distribution will be within one standard deviation (σ) of the mean (μ)?

Answer 27

0.683, or 68.3%

Question 28

Sunset Sarsaparilla is a company that manufactures and bottles various soft drink beverages. They have set up a new machine that fills and seals bottles. The amount of beverage in each bottle follows a normal distribution with a mean (μ) of 20.0 fluid ounces and a standard deviation (σ) of 0.2 ounces. You open a bottle filled by the machine and find it contains 19.35 fluid ounces of beverage. What is the z-score corresponding to 19.35 ounces?

Answer 28

-3.25

Question 29

For the population of customers at the local Department of Licensing, the mean (μ) wait time is 24.4 minutes with a standard deviation (σ) of 5.397 minutes. If you consider taking a random sample of 95 customers, what is the standard deviation of the corresponding sampling distribution?

Answer 29

0.554

Question 30

For the population of undergraduate students enrolled at Seattle University in the 2024-25 academic year, the mean (μ) age is 20.99 with a standard deviation (σ) of 0.89. If you consider taking a random sample of 26 students, what is the mean of the corresponding sampling distribution?

Answer 30

20.99

Question 31

In the 1974 tabletop game Dungeons & Dragons, a player determines their character's Strength score by rolling three six-sided dice and adding them together. This yields a value from 3 to 18 with a mean (μ) of 10.5 and standard deviation (σ) of 2.958. If you took a random sample of 100 Dungeons & Dragons characters, what is the probability that the average Strength score of the sample (x̄) is greater than 11?

Answer 31

0.0455

Question 32

The Blue Ridge Caravan Company runs a regular shipping route from Charleston, WV to Arlington, WV. The number of hours that the route takes follows a normal distribution with a mean (μ) of 2.67 hours and a standard deviation (σ) of 0.22 hours. If a truck takes longer than 3 hours to drive the route, the customer gets a 20% late delivery discount on the shipping fee. What is the probability that the Blue Ridge Caravan Company has to provide the 20% late delivery discount to customers shipping via this route?

Answer 32

0.0668

Question 33

For the population of bottles filled by a machine at the Sunset Sarsaparilla bottling plant, the mean (μ) fill volume is 15.8 ounces with a standard deviation (σ) of 0.16 ounces. If you consider taking a random sample of 61 bottles, what is the standard deviation of the corresponding sampling distribution?

Answer 33

0.020

Question 34

For a standard normal distribution, what is the probability of an observation between -1.645 and 1.645 (shown below)?

Answer 34

0.9000

Question 35

At the Swine & Bovine chain of restaurants in Trumbull Valley, the mean (μ) amount spent by customers during the lunch period (11:00am to 2:00pm) across all of the stores is $16.50 with a standard deviation (σ) of $3.50. The Regional Manager takes a random sample of 100 customer orders during the lunch period. What is the probability that the sample average (x̄) is greater than $17.38?

Answer 35

0.0060

Question 36

For a normal distribution with mean μ and standard deviation σ, what is the probability of an observation less than one standard deviation above the mean (shown below)?

Answer 36

0.8413

Question 37

A 95% Confidence Interval for the mean of (23.5, 31.2) means that there is a 95% probability that the actual population mean falls between 23.5 and 31.2.

Answer 37

False

Question 38

The normal distribution is non-symmetrical and is skewed right.

Answer 38

False

Question 39

Once you have constructed a 95% confidence interval for the mean, there is a 95% probability that the population mean falls within the interval you have constructed.

Answer 39

False

Question 40

Taking a larger sample size will result in a wider confidence interval assuming the sample mean and sample standard deviation are the same.

Answer 40

False

Question 41

When constructing a confidence interval, a higher confidence level (i.e., a lower value for α) will result in a wider interval.

Answer 41

True

Question 42

When taking a sample from a population, a larger sample size will result in a lower variance of the sampling distribution.

Answer 42

True

Question 43

When taking a sample of size n from a population with mean μ and standard deviation σ, what is the standard deviation of the corresponding sampling distribution (σx̄)?

Answer 43

The population standard deviation divided by the square root of the sample size. σ/sqrt n

Question 44

You want to calculate a 95% confidence interval for a mean. Which of the following values for the z-score will you use?

Answer 44

1.96

Question 45

For the population of bottles filled by a machine at the Sunset Sarsaparilla bottling plant, the mean (μ) fill volume is 15.8 ounces with a standard deviation (σ) of 0.16 ounces. If you consider taking a random sample of 39 bottles, what is the mean of the corresponding sampling distribution?

Answer 45

15.80

Question 46

At the Slocum's Joe chain of coffee and donut shops, the automated coffee machine fills 16oz coffee cups with an amount of coffee that follows a normal distribution with a mean (μ) of 15.80oz and a standard deviation (σ) of 0.12oz. A coffee cup is filled by the machine and containes 16.10 ounces of coffee. What is the z-score corresponding to 16.10 ounces?

Answer 46

2.50

Question 47

Corley Motors, a manufacturer of fine motorcycles, has developed a new motorcycle that they want to take to market. After the assembly team learns how to assemble the new model of motorcycle, a random sample of 32 assemblies is observed. For those 32 assemblies, the average (x̄) assembly time was 73.1 minutes; the standard deviation (s) of the sample assembly times was 7.3 minutes. What is the Margin of Error for the associated 95% confidence interval?

Answer 47

2.63

Question 48

For the population of undergraduate students enrolled at Seattle University in the 2024-25 academic year, the mean (μ) age is 20.99 with a standard deviation (σ) of 0.89. If you consider taking a random sample of 57 students, what is the standard deviation of the corresponding sampling distribution?

Answer 48

0.118

Question 49

What is meant by the term “90% confident” when constructing a confidence interval for a mean?

Answer 49

If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

Question 50

The Dean of the Albers School of Business and Economics is concerned that undergraduate business students may not be spending enough time studying statistics per quarter. The Dean decides to take a sample and determine if the mean has decreased since the prior study. In a random sample of 50 students, the average number of hours spent studying statistics per quarter was 190.9. The standard deviation for the population was 42.8 hours. What is the Margin of Error for the associated 99% confidence interval?

Answer 50

15.60

Question 51

The Jelly Bean factory has purchased a new machine for putting jelly beans into jars. The manufacturer indicates that the machine will fill jars with a mean (μ) of 300 beans and a standard deviation (σ) of 12 beans. The manager of the factory takes a random sample of 36 jars and counts the number of jelly beans in each. What is the probability that the sample average (x̄) is less than 295?

Answer 51

0.0062

Question 52

A machine at the Sugar Bombs Breakfast Cereal packaging plant fills boxes of Sugar Bombs cereal such that each box contains 12 ounces of cereal. While some small deviation is allowed, if the mean amount of cereal in boxes goes too far out of specification (either high or low), the machine needs to be shut down for adjustment. The factory manager takes a sample of 40 boxes of Sugar Bombs cereal packed by the machine and weighs how much cereal is in each box. The sample mean (x̄) was 11.89 ounces and the standard deviation (s) was 0.31 ounces. What is the Point Estimate for the associated 95% confidence interval?

Answer 52

11.890

Question 53

A candy factory has purchased a new machine to place candies into a bag. In order to properly calibrate the machine, the factory manager first has to determine the mean number of candies being placed in bags before the machine can be adjusted. The factory manager takes a sample of 50 bags packed by the machine and calculates a sample mean (x̄) of 55.4 candies and a sample standard deviation (s) of 0.4 candies. What is the Margin of Error for the associated 95% confidence interval?

Answer 53

0.11

Question 54

The manager of the Spencer's Mill location of the Swine & Bovine restaurant chain in Trumbull Valley is interested in the average amount that customers spend at the restaurant. In order to answer this question, they take a sample of 50 customer orders. That sample mean (x̄) was $17.35 with a standard deviation (s) of $5.31. What is the Point Estimate for the associated 95% confidence interval?

Answer 54

17.35