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# MATH 533 Final Exam v2

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Author: Abraham Nolito
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1. (TCO A)A random sample of 20 cars driving down I-294 is selected and their speed is monitored. The results are as follows (in mph).
68 65 50 79 77 60 55 61 78 75
75 67 72 58 70 62 67 72 70 74

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on speed per car
2. (TCO B) Consider the following data on newly hired employees in relation to which part of the country they were born and their highest degree attained.

HS

BS

MS

PHD

Total

East

3

5

2

1

11

Midwest

7

9

2

0

18

South

5

8

6

2

21

West

1

7

8

6

22

Total

16

29

18

9

72

If you choose one person at random, then find the probability that the person

a. has a PHD
b. is from the East and has a BS as the highest degree attained.
3. (TCO B)A source in the Internal Revenue Service has stated that historically 90% of federal tax returns filed are free of arithmetic errors. A random sample of 25 returns are selected and checked carefully for arithmetic errors. Assuming independence, find the probability that
4. (TCO B)CJ Computer Disks stocks and sells recordable CDs. The monthly demand for these CDs is closely approximated by a normal distribution with a mean of 20,000 disks and standard deviation of 4,000 disks. CJ receives shipments from the supplier once per month (at the beginning of each month).

a. Find the probability that the demand for recordable CDs exceeds 30,000 for a particular month
b. Find the probability that the demand for recordable CDs is between 12,000 and 18,000
c. How large an inventory must CJ have available at the beginning of the month so that the probability of running out of recordable CDs (a stock out) during the month is no more than .05? (Points : 18)
5. (TCO C) The Ford Motor Company wishes to estimate the mean dollar amount of damage done to a Ford Explorer as a result of a 10 mph crash into the rear bumper of a parked car. The sample results are as follows.

Sample Size = 36
Sample Mean = \$638
Sample Standard Deviation = \$115
6. (TCO C) A clock company is concerned about errors in assembly of their custom made clocks. A random sample of 120 clocks from today’s production yields nine clocks with assembly errors.
7. (TCO D) The Cottrell Soap Company has produced a new dish washing liquid that it believes is superior to competitive products on the market. The board of directors has indicated that the product will be marketed if more than 25% of the population of households prefer the product over its competitors. The company’s market research department has distributed the new product to 400 randomly selected households. The results of this sampling are that 120 of the 400 households prefer the new dish washing liquid. Does the sample data provide evidence to conclude that the percentage of households in the population that prefer the new dishwashing liquid is more than 25% (with a = .05)? Use the hypothesis testing procedure outlined below
8. (TCO D) A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 shoes leads to the following results in terms of useful life.

Sample Size = 36 shoes
Sample Mean = 52.3 hours
Sample Standard Deviation = 9.6 hours

(more)
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