# MATHEMATICS

14. On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

A. 1/5 B. 1/6 C. 1/4 D. 2/5

P(correct) = Number of correct answers / Number of possible choices

P(correct) = 1/6

15. A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What does this mean?

A. The improvement was due to the fact that there were more weeds in one study.

B. The probability that the difference was due to chance alone is greater than 0.05.

C. The probability that one weed killer performed better by chance alone is less than 0.05.

D. There is not enough information to make any conclusion.

16. The distribution of B.A. degrees conferred by a local college is listed below, by major.

Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly selected degree is not in Business?

A. 0.7800 B. 0.8200 C. 0.8300 D. 0.9200

P(not in Business) = (Number not in Business) / Total number of degrees

P(not in Business) = (9313 – 1676) / 9313

P(not in Business) = 0.8200

17. A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man’s expected value for the insurance policy?

A. $139,916 B. −$41 C. $84 D. −$124

E(x) = (1 – 0.9994)($140,000) – $125 = -$41

18. A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A. 2/11 B. 3/11 C. 5/14 D. 3/14

P(blue) = Number of blue marbles / Total number of marbles

P(blue) = 3 / (4 + 3 + 7) = 3/14

19. The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.

112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000

140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000

A. 0.4 B. 0.6 C. 0.66 D. 0.7

P(salary ≥ $98,000) = Number of salaries ≥ 98,000 / Total number of salaries

P(salary ≥ $98,000) = 14/20 = 0.7