Probability and Statistics Flashcards
The standard deviation of the numbers 4, 9, 13, 18 and 26 is 7.56, correct to two decimal places. What will be the standard deviation if each of the five numbers is increased by 3?
A. 10.56
B. 7.56
C. 4.56
D. 3
Correct Option: B
The winning scores in US soccer from 1972 to 1981 were as follows: 34, 28, 77, 22, 29, 34, 81, 28, 28, and 77. Find the mean, median, and mode of these scores.
A. 43.8, 31.5, 28
B. 53.7, 15.5, 28
C. 34.5, 23.5, 28
D. 24, 34.5, 28
Correct Option: A
The manager of the public library is interested in how many people spend time at the library during lunchtime. He writes down data for 10 selected days: 44, 50, 38, 96, 42, 47, 40, 39, 46, 50. What are the mean and sample standard deviation of these data?
A. 52, 17
B. 49.2, 17
C. 49.2, 15
D. 43, 17
Correct Option: B
The number of miles walked by six neighbors in one week is 18, 22, 16, 30, 17, and 22. Which of the following answers is the mean of this data set?
A. 20.83
B. 32.13
C. 22.15
D. 20.02
Correct Option: A
Hint: On a CASIO FX-115ES calculator, follow the steps below to calculate the mean:
1. MODE
2. 3- FOR STAT
3. 1 – FOR VAR
4. INPUT NUMBERS Followed by =
5. ON
6. SHIFT Followed by the number 1
7. 5 – FOR VAR
8. 2 – FOR MEAN
9. =
Henry got an average score of 89 on three tests. What score must he get on the fourth test so that his average score on the four tests will become 90?
A. 89
B. 92
C. 93
D. 100
Correct Option: C
The sum of Henry’s scores on the first three tests is 3 × 89 = 267. The sum of four tests with a score of 90 is 4 × 90 = 360.
Therefore, Henry’s score on the fourth test must be 360 – 267 = 93 to reach an average of 90.
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Find the standard deviation of a population of data of 54, 66, 76, 12, 10, 89, 15, 16, 4, and 6.
A. 26.33
B. 33.89
C. 31.04
D. 45.16
Correct Option: C
Hint: On a CASIO FX-115ES calculator, follow the steps below to calculate the mean:
1. MODE
2. 3- FOR STAT
3. 1 – FOR VAR
4. INPUT NUMBERS Followed by =
5. ON
6. SHIFT Followed by the number 1
7. 5 – FOR VAR
8. 3 – STD DEVIATION
9. =
What is the sample standard deviation of the following numbers?
6, 9, 6, 7, 2, 62, 54, 26, 19, 30
A. 21.13
B. 31
C. 32.5
D. 34
Correct Option: A
What are the mean and standard deviation for the following set of data?
1, 3, 8, 45, 58, 48, 19, 15, 91, 16, 43, 44, 2, 96, 10
A. Mean =33.27, Standard Deviation =29.88
B. Mean =23.72, Standard Deviation =29.88
C. Mean =33.27, Standard Deviation =28.88
D. Mean =29.88, Standard Deviation =33.27
Correct Option: A
Solution:
On a Casio FX-115ES calculator, do the following to find the mean:
- MODE
- 3 – FOR STAT
- 1 – FOR VAR
- INPUT NUMBERS (foloowed by =)
- ON
- SHIFT (followed by the number 1)
- 5 – FOR VAR
- 2 – FOR MEAN
- Do the following to find the standard deviation:
- SHIFT (followed by the number 1)
- 5 – FOR VAR
- 3 – STD DEVIATION
Find variance for the following student weights:
135, 150, 120, 180, 145
A. 500
B. 456
C. 150
D. 394
Correct Option: D
Solution:
On a Casio FX-115ES calculator, do the following
- MODE
- 3 – FOR STAT
- 1 – FOR VAR
- INPUT NUMBERS (followed by =)
- ON
- SHIFT
- PRESS 1
- 5 – FOR VAR
- 3 – STD DEVIATION
- EQUAL AND POWER 2
Sample variance: Square of the standard deviation, s:
A bag contains ten balls, marked with the numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, and 4, respectively. Suppose the probability of each ball being selected is equal. Determine the expected value of a discrete random variable X.
A. 1
B. 2
C. 3
D. 4
Correct Option: C
Suppose a random variable X is uniformly distributed on the range [3, 6]. Let Y = X + 2. Determine the expected value of Y.
A. 4.0
B. 4.5
C. 6.5
D. 8.5
Correct Option: C
What can a 95% confidence interval for a population mean be interpreted as?
A. In 95% of the samples, the sample mean will be outside of the interval.
B. There is a 5% chance that the true population mean is outside of the interval.
C. Ninety-five percent of all population means is within the interval.
D. Both A and B
Correct Option: B
Solution:
A confidence interval (CI) is a type of interval estimate of a population parameter, which may include the unknown population parameter with a specified level of probability. A 95% confidence interval for a parameter μ means that there is a 95% probability that the interval constructed from sample data will include the unknown parameter μ. In other words, there is a 95% probability that the parameter μ is within the confidence interval.
A) is incorrect. The confidence interval is for population mean, not for sample mean.
B) is correct.
C) is incorrect. There is only one population mean.
D) is incorrect, since A) is incorrect.
Five random samples are taken from a normally distributed population. To construct a confidence interval for the population mean, what distribution should the confidence interval be based upon if the population variance is known?
A. normal
B. t
C. chi-square
D. F
Correct Option: A
Assuming the population variance is known, what will happen to the width of a confidence interval for a population parameter change when the sample size increases (with everything else remaining the same)?
A. It will increase.
B. It will decrease.
C. It will remain unchanged.
D. Sometimes it will increase and sometimes it will decrease.
Correct Option: B
A sample of size 25 is randomly taken from a normally distributed population, and gives a mean of 13 and a standard deviation of 3. Construct an 80% confidence interval for the population mean.
A. [11.824, 14.176]
B. [11.824, 13.769]
C. [12.231, 13.769]
D. [12.231, 14.176]
Correct Option: C
