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There are 25 problems. Problems #1–12...

There are 25 problems.

Problems #1–12 are Multiple Choice.

Problems #13–15 are Short Answer. (Work not required to be shown)

Problems #16–25 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Max purchases a car for $26,000, makes a down payment of 15%, and finances the rest with a

5-year car loan at an annual interest rate of 4.8% compounded monthly. What is the amount of

his monthly loan payment?

1. _______

A. $456.73

B. $415.03

C. $537.33

D. $488.27

4. The cholesterol levels of a population of adults are normally distributed, with a mean of 196 mg/dL and a standard deviation of 34 mg/dL. What is the probability that a randomly chosen adult has a cholesterol level between 162 and 230 mg/dL?

A. 0.5000

B. 0.6826

C. 0.7580

D. 0.9544

For #6 and #7:

A merchant makes two raisin nut mixtures.

Each box of mixture A contains 15 ounces of peanuts and 3 ounces of raisins, and sells for $5.10.

Each box of mixture B contains 8 ounces of peanuts and 4 ounces of raisins, and sells for $3.60.

The company has available 6,200 ounces of peanuts and 2,000 ounces of raisins. The merchant

will try to sell the amount of each mixture that maximizes income.

Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B.

6. State the objective function.

A. 5.1x + 3.6y

B. 15x + 3y

C. 15x + 8y

D. 23x + 7y

7. Since the merchant has 2,000 ounces of raisins available, one inequality that must be satisfied

is:

A. 3x + 4y £ 2,000

B. 3x + 4y ³ 2,000

C. 7x £ 2,000

D. 5.1x + 3.6y ³ 2,000

8. A jar contains 16 red jelly beans, 20 yellow jelly beans, and 12 orange jelly beans.

Suppose that each jelly bean has an equal chance of being picked from the jar.

If a jelly bean is selected at random from the jar, what is the probability that it is not red?

A. 1/3 B. ½ C. 2/3 D. ¾

10. Which of the following statements is NOT true?

A. The variance can be a negative number.

B. The variance is a measure of the dispersion or spread of a distribution about its mean.

C. The standard deviation is the square root of the variance.

D. If all of the data values in a data set are identical, then the standard deviation is 0.

11. In a certain manufacturing process, the probability of a type I defect is 0.10, the probability

of a type II defect is 0.05, and the probability of having both types of defects is 0.02.

Find the probability that neither defect occurs.

A. 0.83

B. 0.85

C. 0.87

D. 0.98

12. Which of the following is NOT true?

A. A probability must be less than or equal to 1.

B. If events E and F are independent events, then P(E Ç F) = 0.

C. If only two outcomes are possible for an experiment, then the sum of the probabilities of

the outcomes is equal to 1.

D. If an event cannot possibly occur, then the probability of the event is 0.

SHORT ANSWER:

13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}. Let A = {2, 4, 7, 8} and B = {1, 2, 3, 4}.

Determine the set A' Ç B. Answer: ______________

(Be sure to notice the complement symbol applied to A.)

15. 400 employees at a particular company were asked their status (full-time or part-time)

and their primary means of transportation to and from work. The following table was obtained.

(Primary-Transportation) Full-time Part-time Total

Car 188 60 248

Bus 32 44 76

Subway 30 27 57

On Foot 10 9 19

Total 260 140 400

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly selected employee:

(a) travels by bus and is full-time. Answer: ______________

(b) travels by bus or is full-time. Answer: ______________

(c) travels by bus, given that the employee is full-time. Answer: ______________

SHORT ANSWER, with work required to be shown, as indicated.

16. For a six year period, Ralph deposited $600 each quarter into an account paying 6.4% annual

interest compounded quarterly. (Round your answers to the nearest cent.)

(a) How much money was in the account at the end of 6 years? Show work.

(b) How much interest was earned during the 6 year period? Show work.

Ralph then made no more deposits or withdrawals, and the money in the account continued to

earn 6.4% annual interest compounded quarterly, for 7 more years.

(c) How much money was in the account after the 7 year period? Show work.

(d) How much interest was earned during the 7 year period? Show work.

17. An artist has a portfolio of 16 paintings and plans to display three of the paintings in a row

(left, middle, right) on the wall of an art gallery. How many different arrangements of paintings

Problems #1–12 are Multiple Choice.

Problems #13–15 are Short Answer. (Work not required to be shown)

Problems #16–25 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Max purchases a car for $26,000, makes a down payment of 15%, and finances the rest with a

5-year car loan at an annual interest rate of 4.8% compounded monthly. What is the amount of

his monthly loan payment?

1. _______

A. $456.73

B. $415.03

C. $537.33

D. $488.27

4. The cholesterol levels of a population of adults are normally distributed, with a mean of 196 mg/dL and a standard deviation of 34 mg/dL. What is the probability that a randomly chosen adult has a cholesterol level between 162 and 230 mg/dL?

A. 0.5000

B. 0.6826

C. 0.7580

D. 0.9544

For #6 and #7:

A merchant makes two raisin nut mixtures.

Each box of mixture A contains 15 ounces of peanuts and 3 ounces of raisins, and sells for $5.10.

Each box of mixture B contains 8 ounces of peanuts and 4 ounces of raisins, and sells for $3.60.

The company has available 6,200 ounces of peanuts and 2,000 ounces of raisins. The merchant

will try to sell the amount of each mixture that maximizes income.

Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B.

6. State the objective function.

A. 5.1x + 3.6y

B. 15x + 3y

C. 15x + 8y

D. 23x + 7y

7. Since the merchant has 2,000 ounces of raisins available, one inequality that must be satisfied

is:

A. 3x + 4y £ 2,000

B. 3x + 4y ³ 2,000

C. 7x £ 2,000

D. 5.1x + 3.6y ³ 2,000

8. A jar contains 16 red jelly beans, 20 yellow jelly beans, and 12 orange jelly beans.

Suppose that each jelly bean has an equal chance of being picked from the jar.

If a jelly bean is selected at random from the jar, what is the probability that it is not red?

A. 1/3 B. ½ C. 2/3 D. ¾

10. Which of the following statements is NOT true?

A. The variance can be a negative number.

B. The variance is a measure of the dispersion or spread of a distribution about its mean.

C. The standard deviation is the square root of the variance.

D. If all of the data values in a data set are identical, then the standard deviation is 0.

11. In a certain manufacturing process, the probability of a type I defect is 0.10, the probability

of a type II defect is 0.05, and the probability of having both types of defects is 0.02.

Find the probability that neither defect occurs.

A. 0.83

B. 0.85

C. 0.87

D. 0.98

12. Which of the following is NOT true?

A. A probability must be less than or equal to 1.

B. If events E and F are independent events, then P(E Ç F) = 0.

C. If only two outcomes are possible for an experiment, then the sum of the probabilities of

the outcomes is equal to 1.

D. If an event cannot possibly occur, then the probability of the event is 0.

SHORT ANSWER:

13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}. Let A = {2, 4, 7, 8} and B = {1, 2, 3, 4}.

Determine the set A' Ç B. Answer: ______________

(Be sure to notice the complement symbol applied to A.)

15. 400 employees at a particular company were asked their status (full-time or part-time)

and their primary means of transportation to and from work. The following table was obtained.

(Primary-Transportation) Full-time Part-time Total

Car 188 60 248

Bus 32 44 76

Subway 30 27 57

On Foot 10 9 19

Total 260 140 400

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly selected employee:

(a) travels by bus and is full-time. Answer: ______________

(b) travels by bus or is full-time. Answer: ______________

(c) travels by bus, given that the employee is full-time. Answer: ______________

SHORT ANSWER, with work required to be shown, as indicated.

16. For a six year period, Ralph deposited $600 each quarter into an account paying 6.4% annual

interest compounded quarterly. (Round your answers to the nearest cent.)

(a) How much money was in the account at the end of 6 years? Show work.

(b) How much interest was earned during the 6 year period? Show work.

Ralph then made no more deposits or withdrawals, and the money in the account continued to

earn 6.4% annual interest compounded quarterly, for 7 more years.

(c) How much money was in the account after the 7 year period? Show work.

(d) How much interest was earned during the 7 year period? Show work.

17. An artist has a portfolio of 16 paintings and plans to display three of the paintings in a row

(left, middle, right) on the wall of an art gallery. How many different arrangements of paintings

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