### Finish 25 statistic questions

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1.Consider the following sample of five LSAT scores:

 155 155 150 180 175

Compute the 40th percentile score.

(a) 155(b) 160(c) 160.5(d) 167.5(e) none of these responses

2.Consider the below data on years of education and earnings.

 Years of Education 13 17 12 21 22 Earnings (in 1000’s) \$25 \$55 \$20 \$80 \$100

Compute the correlation coefficient between years of education and earnings.

(a) .793(b) -.922(c) 3.96(d) .922(e) .990

Answer questions 3 – 5 using the following:

30% of the employees of a company are college graduates.Of those who did not graduate college, 20% are in supervisory positions.Of those who graduated college, 70% are in supervisory positions.

3.Of those who did not graduate college, what percent are not in supervisory positions?

(a) 75%(b) 80%(c) 30% (d) 25%(e) 25.7%

4. What percent of the employees are supervisors and college graduates?

(a) 70%(b) 14%(c) 100%(d) 90%(e) 21%

5. What is the probability that a randomly selected supervisor is not a college graduate?

(a) .400(b) .600(c) .745(d) .140(e) .210

6. In a horse race, 15 horses are running.You are gambling.You have purchased a ticket that requires you to select 4 horses as first, second, third, and fourth place winners.To win, the 4 horses that you selected must finish the race in that order.What is the probability of you winning?

(a) 1/2730(b) 1/5(c) 1/455(d) 1/3375(e) none of these responses

For questions 7 – 12, consider the experiment of rolling a six-sided die once and recording the outcome.This is a standard die – each of the six sides of the die contains a different number from the set of numbers {1, 2, 3, 4, 5, 6}.

7. Define event A = {1, 2} and event B = {2, 4, 5}.What is A Ç B?

(a) {1, 2, 4, 5}(b) {2}(c) {1, 2, 2, 4, 5}(d) {1, 4, 5}(e) none of these responses

8.Refer to question 7.Compute P(A) and P(B).

(a) P(A) = 1/2, P(B) = 3/4(b) P(A) = 3/4, P(B) = 1/2(c) P(A) = 1/3, P(B) = 1/2(d) none of these responses

9. Refer to question 7.Compute P(A|B).

(a) 1/2(b) 1/3(c) 3/4(d) 2/3(e) 1

10. Refer to question 7.Compute P(B|A).

(a) 1/2(b) 1/3(c) 3/4(d) 2/3(e) 1

11. Refer to question 7.Are A and B independent?

(a) Yes(b) No

12. Refer to question 7.Are A and B mutually exclusive?

(a) Yes(b) No

13. Given P(A) = .35, P(B) = .22, and P(AÇB) = .1, compute P(A|B).

(a) .100(b) .022(c) .035(d) .455(e) .286

14. In a family of 6 children, what is the probability that there will be exactly 2 boys?You should assume that the probability of having a boy always equals that of having a girl equals.5.

(a) .333(b) .375(c) .234(d) .469(e) .938

15. Refer to question 14.Compute the expected number of boys.

(a) 0(b) 1(c) 2(d) 3(e) 4

Answer questions 16 – 17 based on the following:

An insurance company has determined that each week an average of four claims are filed in their Atlanta branch.

16. What is the probability that during the next week no claims will be filed?

(a) 0(b) .0732(c) .0498(d) .0183(e) 54.598

17. What is the probability that during the next week two or more claims will be filed?

(a) .1464(b) .0732(c) .0915(d) .8010(e) .9085

18. Suppose that the hardness of steel is uniformly distributed, taking on values between 50 and 80 on the Rockwell B scale.Compute the probability that the hardness of a randomly selected steel specimen is less than 65.

(a) .462(b) .333(c) .500(d) 2(e) .750

19. Refer to question 18.Compute the expected steel hardness.

(a) 130(b) 30(c) 60(d) 15(e) 65

20. The life expectancy of a particular brand of hair dryer is normally distributed with a mean of 48 months and a standard deviation of 12 months.Ninety percent of the hair dryers will have a life expectancy of at least how many months?

(a) 28.3(b) 32.6(c) 46.4(d) 67.7(e) 49.6

21. The number of electrical outages in a city varies from day to day.Assume that the number of electrical outages (x) in the city has the following probability distribution:

 x f(x) 0 0.80 1 0.15 2 0.04 3 0.01

Compute the mean number of electrical outages.

• 2.6(b) 0.26(c) 3(d) 0

22. Refer to question 21.Compute the standard deviation.

(a) 5.77(b) 0.577(c) 0.01(d) 0.8

Answer questions 23 and 24 based on the following:

The mean annual cost of automobile insurance is \$939.The standard deviation is \$300.You have been asked to compute the probability that a simple random sample of automobile insurance policies of size 100 will have a sample mean within \$30 of the population mean.

23. Compute the standard deviation of the population.

(a) \$300(b) \$3(c) \$1.73(d) \$5.48(e) \$30

24. Compute the probability that a simple random sample of automobile insurance policies of size 100 will have a sample mean within \$30 of the population mean.

(a) .0638(b) .0319(c) .5934(d) .2967(e) .6826

25. Which of the following is not a characteristic of the normal distribution?

(a) the mean, median and mode are equal(b) the mean of the distribution can be negative, zero, or positive(c) the distribution is symmetrical(d) the standard deviation must be 1

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