FINAL EXAM AND HOMEWORK7

Name _______________________________________

MBA 501 Math & Stats for Business

Week 14 In-class Assignment

Instructions

1. This assignment is to be done individually . This is not a group assignment.

1. The In-class assignment is due in the end of the class.

1. Only explained and detailed answers will be accepted.

1. Use the back of the page for calculations

1. A normal distribution of scores has a standard deviation of 10. Find the z-scores corresponding to each of the following values: ( 1 Point Each )

a) A score that is 20 points above the mean.

b) A score that is 10 points below the mean.

c) A score that is 15 points above the mean.

d) A score that is 30 points below the mean.

2. For the numbers below, find the area between the mean and the z-score: ( 1 Point Each )

a) z = 1.17

b) z = -1.37

3. For a normal distribution, find the z-score that separates the distribution as follows: ( 1 Point Each )

a) Separate the highest 30% from the rest of the distribution.

b) Separate the lowest 40% from the rest of the distribution.

c) Separate the highest 75% from the rest of the distribution.

4. Pat and Chris both took a spatial abilities test (mean = 80, std. dev. = 8). Pat scores a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris? ( 2 Points )

5. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160. ( 1 Point Each )

a) What is the difference between Einstein’ IQ and the mean?

b) How many standard deviations is that?

c) Convert Einstein’s IQ score to a z score.

d) If we consider “usual IQ scores to be those that convert z scores between -2 and 2, is Einstein’s IQ usual or unusual?

6. A state department of corrections has a policy whereby it accepts as correctional officers only those who score in the top 5 % of a qualifying exam. ( 5 Points )

The mean of this test is 80.

Standard deviation is 10.

a) Would a person with a raw score of 95 be accepted? ( Hint: Calculate a Z score: score – mean/st.dev. = )

b) Given a normal distribution of raw scores with a mean of 60 and a standard deviation of 8, what proportion of cases fall:

a) between a raw score of 50 and 80?

b) between a raw score of 48 and 57?