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MATH 533 Final Exam

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Author: Abraham Nolito
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1. (TCO A)Consider the following sample data on the age of the 30 employees that were laid off recently from DVC Inc.
21 38 20 26 37 52 37 24 45 20
50 49 44 30 29 42 56 46 60 30
32 25 47 55 38 25 20 29 32 30

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on age of employees being laid off.

b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)
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.

c. has only a HS degree, given that person is from the West. (Points : 18)
3. (TCO B) Squib claims that its new pain reliever is effective in giving relief for headaches within 10 minutes for 95% of users. A random sample of 25 patients is selected. Assuming Squibb is correct, then find the probability that

a. exactly 23 patients obtain relief within 10 minutes.
b. more than 23 patients obtain relief within 10 minutes.
c. at most 22 patients obtain relief within 10 minutes. (Points : 18)
4. (TCO B) At a local supermarket the monthly customer expenditure follows a normal distribution with a mean of \$495 and a standard deviation of \$121.

a. Find the probability that the monthly customer expenditure is less than \$300 for a randomly selected customer

b. Find the probability that the monthly customer expenditure is between \$300 and \$600 for a randomly selected customer.
c. The management of a supermarket wants to adopt a new promotional policy giving a free gift to every customer who spends more than a certain amount per month at this supermarket. Management plans to give free gifts to the top 8% of its customers (in terms of their expenditures). How much must a customer spend in a month to qualify for the free gift? (Points : 18)
5. (TCO C) A tool manufacturing company wants to estimate the mean number of bolts produced per hour by a specific machine. A simple random sample of 9 hours of performance by this machine is selected and the number of bolts produced each hour is noted. This leads to the following results.

Sample Size = 9
Sample Mean = 62.3 bolts/hr
Sample Standard Deviation = 6.3 bolts/hr

a. Compute the 90% confidence interval for the average number bolts produced per hour
b. Interpret this interval.
c. How many hours of performance by this machine should be selected in order to be 90% confident of being within 1 bolt/hr of the population mean number of bolts per hour by this specific machine? (Points : 18)
6. (TCO C) A clock company is concerned about errors in assembly in their custom made clocks. A simple random sample of 120 clocks yields nine clocks with errors in assembly.

a. Compute the 99% confidence interval for the proportion of clocks with errors in assembly
b. Interpret this confidence interval.
c. How large a sample size will need to be selected if we wish to have a 99% confidence interval that is accurate to within 1.5%? (Points : 18)

(more)
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