# (3 points) on an exam with a mean of m = 82, you obtain a score of x

1**. (3 points) On an exam with a mean of ****M**** ****= 82, you obtain a score of ****X*** ***=86.**

**a. Would you prefer a standard deviation of ****s**** ****= 2 or ****s**** ****= 10? (****Hint****: Sketch each distribution and find the location of your score.)**

**b. If your score were ****X = 78,*** ***would you prefer ****s**** ****= 2 or ****s = 10? ****Explain your answer.**

2. **(3 points) A student was asked to compute the mean and standard deviation for the following sample of ****n**** ****= 5 scores: 81, 87, 89, 86, and 87. To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7. The mean and standard deviation for the new sample were then calculated to be ****M**** ****= 6 and ****x**** ****= 3. What are the values of the mean and standard deviation for the original sample?**

3. (3 points)

**Calculate ****SS****, variance, and standard deviation for the following population of ****N**** ****= 7 scores: 8, 1, 4, 3, 5, 3, 4. (****Note:*** ***The definitional formula works well with these scores.)**

4. **(3 points) For the following population of ****N**** ****= 6 scores: 5, 0, 9, 3, 8, 5**

a. Sketch a histogram showing the population distribution.

**a. ****Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example, 4.2).**

** **

**b. ****Compute ****SS****, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of σ?)**

**5. (3 points) A distribution has a standard deviation of σ = 12. Find the ****z****-score for each of the following locations in the distribution.**

a. Above the mean by 3 points.

b. Above the mean by 12 points.

c. Below the mean by 24 points.

d. Below the mean by 18 points.

**6. (5 points) For a population with a mean of µ = 100 and a standard deviation of 12**

**a. Find the ****z****-score for each of the following ****X**** ****values.**

*X** *= 106 *X** *= 115 *X** *= 130

*X** *= 91

*X** *= 88

*X** *= 64

**b. Find the score (****X**** ****value) that corresponds to each of the following ****z****-scores.**

*z* = – 1.00

*z* = – 0.50

*z* = 2.00 *z* = 0.75

*z* = 1.50

*z* = – 1.25

**7. (3 points) Find the ****z****-score corresponding to a score of ****X**** ****= 60 for each of the following distributions.**

a. µ = 50 and σ = 20

b. µ = 50 and σ = 10

c. µ = 50 and σ = 5

d. µ = 50 and σ = 2

**8. (1 point) A score that is 6 points below the mean corresponds to a ****z****-score of ****z**** ****= – 0.50. What is the population standard deviation?**

**9. (3 points) For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.**

**a. A score of ****X*** ***= 56, on an exam with µ = 50 and σ = 4, or a score of ****X**** ****= 60 on an exam with µ = 50 and σ = 20.**

**b. ****A score of ****X*** ***= 40, on an exam with µ = 45 and σ = 2, or a score of ****X**** ****= 60 on an exam with µ = 70 and σ = 20.**

**c. A score of ****X*** ***= 62, on an exam with µ = 50 and σ = 8, or a score of ****X**** ****= 23 on an an exam with µ = 20 and σ = 2.**

**1. For the following set of scores, find the value of each expression. (5 points)**

*X*

-4

-2

0

-1

-1

**2. Construct a frequency distribution table for= the following set of scores. Include columns for proportion and percentage in your table. (5 points)**

**Scores: 5, 7, 8, 4, 7, 9, 6, 6, 5, 3, 9, 6, 4, 7, 7, 8, 6, 7, 8, 5**

**3. The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New York during 2008. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your= table, does in appear the tickets are issued equally across age groups? (5= points)**

17, 30, 45, 20, 39, 53,28, 19

24, 21, 34, 38, 22, 29, 64

22, 44, 36, 16, 56, 20, 23, 58

32, 25, 28, 22, 51, 26, 43

No the tickets are not distributed equally among all age groups.

**4. Find the mean, median, and mode for the scores in the following frequency distribution table. (5 points)**

**_____**

* X *** f f*X cf **

** **

**10 1 10 15**

** 9 2 18 14**

** 8 3 24 12**

** 7 3 21 9**

** 6 4 24 6**

** 5 2 10 2**