# Probability and Statistics

1. TFQ: Amy wants to find a 96% confidence interval for the amount of time it takes to get to work. She kept records for 35 days and found her average time to commute to work was 20.5 minutes with a standard deviation of 3.6 minutes. Amy's maximum error of estimate would be 1.25 minutes.

2. TFQ: Charles wants to be 90% confident that the true mean of his population is within 3 units. The standard deviation is assumed to be 8 units. Charles should use a minimum of 17 people in his sample.

3. MCQ: An economics professor randomly selected 100 millionaires in the U.S. The average age of these millionaires was 52.1 years with a standard deviation of 12.3 years. What is a 99% confidence interval for the mean age, m, of all U.S. millionaires?

a) 50.1 < m < 54.1 b) 51.9 < m < 52.4 c) 49.7 < m < 54.5

d) 48.9 < m < 55.3 e) NOT

4. MCQ: A lawyer researched the average number of years served by 40 different justices on the Supreme Court. The average number of years served was 14.8 years with a standard deviation of 7.8 years. What is the 95% confidence interval for the average number of years served by all Supreme Court justices?

a) 12.8 < m < 16.8 b) 12.4 < m < 17.2 c) 11.9 < m < 17.7

d) 11.6 < m < 18.0 e) NOT

5. TFQ: A statistician wanted to find a 99% confidence interval using the t-distribution. If n = 18, the table value would be 2.898 .

6. TFQ: The value for  2left for a 95% confidence interval when n = 16 is 6.908 .

7. MCQ: A vending machine distributor wants to be 99% confident that the coffee machine is dispensing the correct amount of coffee to within 0.15 fluid ounces. If it is known that the standard deviation is 0.32 fluid ounces, how many cups of coffee should be measured?

a) 13 b) 23 c) 31 d) 45 e) NOT

8. MCQ: The average cost of living for a family of 4 in twelve different cities was found to be $65,351 with a standard deviation of $7711. What is a 95% confidence interval for the true mean?

a) $60,452 < m < $70,250 b) $60,988 < m < $69,714

c) $61,745 < m < $68,957 d) $62,324 < m < $68,378

e) NOT

9. TFQ: Fred wants to calculate the 98% confidence interval around the mean using the z-distribution. His sample of 64 items has a mean of 35 and a standard deviation of 6. The maximum error of estimate would not change if the mean were 25 instead of 35, but the sample size, standard deviation and confidence interval remained the same.

10. MCQ: The average life expectancy of citizens in 22 different Asian countries was reported to be 62.3 years with a standard deviation of 3.9 years. What is the 99% confidence interval for the true mean?

a) 60.2 < m < 64.4 b) 60.7 < m < 63.9

c) 59.9 < m < 64.7 d) 58.4 < m < 66.2

e) NOT

11. MCQ: A tax firm wants to determine the percentage of Americans who get professional help with their tax returns. They wish to be 95% confident that the estimate is within 2.5%. How large should the sample size be, if it is estimated that 36% of Americans get professional help in preparing their tax returns?

a) 1089 b) 1417 c) 998 d) 604 e) NOT

12. MCQ: A sample of 60 faculty members at a large university found that their average taxes were $550 a month, with a standard deviation of $40. What is the 95% confidence interval of the average taxes of all faculty members at the university?

a) 525 < m < 575 b) 542 < m < 558

c) 537 < m < 563 d) 540 < m < 560

e) NOT

13. TFQ: A confidence interval was constructed around a proportion. The interval was from 21.7% to 36.1%. The proportion that was used to construct this interval was 28.9%.

14. TFQ: A retailer wants to estimate with 99% confidence the number of people who buy at his store. A previous study showed that 19% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 1135 .

15. MCQ: A tornado has blown through a section of Collinsville. The insurance adjuster wants to estimate the average claim to within $500. If the standard deviation is believed to be $1650 and the company wants to be 95% sure of their figures, how large a sample must be taken?

a) 123 b) 42 c) 68 d) 189 e) NOT

16. TFQ: The probability is 1 that the total area under the standard normal curve is 1.0 .

17. VISA reported with 95% confidence that 19% of those surveyed used checks to pay for purchases. If 946 people participated in the survey, what was the percentage of error?

a) 3% b) 2.5% c) 1.4% d) 2% e) NOT

18. TFQ: For 12 years, a meteorologist kept track of the number of days it snowed in February. The results were as follows: 4, 5, 12, 2, 9, 10, 6, 5, 8, 15, 2, 9. The 98% confidence interval of the true mean is

4.7 < m < 9.8 .

19. TFQ: A sample of 300 racing cars showed that 90 cost over $500,000. The 95% confidence interval of the true proportion of cars costing over $500,000 is 0.257 < p < 0.343 .

20. MCQ: What is the value for  2 right for a 90% confidence interval when n = 16 ?

a) 7.962 b) 7.261 c) 24.996 d) 26.296 e) NOT

21. TFQ: There is a probability  that a z score will have a value between -z/2 and z/2 .

22. TFQ: Correct to at least 6 decimal places, the area under a standard normal curve between z = 5 and z = 6 is 2.86 .

23. MCQ: What is the 99% confidence interval for the standard deviation of birth weights at County General Hospital, if the standard deviation of the last 22 babies born there was 1.5 pounds?

a) 1.1 <  < 2.4 b) 1.2 <  < 2.1 c) 1.2 <  < 2.0

d) 1.1 <  < 2.3 e) NOT

24. MCQ: What is the best point estimate of the range of the population?

a) mode of the sample b) mean of the sample

c) median of the sample d) standard deviation of the sample

e) NOT

25. TFQ: To find a chi-square left value for a 90% confidence interval, one should use the column headed 0.90 .

26. TFQ: When the variable is normally distributed, the sample size is greater than 30, but only the sample standard deviation is known, then the t distribution must be used to find confidence intervals for the mean.

27. MCQ: The manager of the dairy store wants to determine the proportion of people who buy milk each day. During one day, 150 out of 250 people bought milk. What is the 99% confidence interval for the true proportion of customers who buy milk each day?

a) 0.51 < p < 0.69 b) 0.52 < p < 0.68 c) 0.54 < p < 0.66

d) 0.55 < p < 0.65 e) NOT

28. MCQ: The average hourly wage of workers in a fast food restaurant is $5.85 with a standard deviation of $0.35. Assume that the distribution is normal. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns between $5.50 and $6.50 an hour?

a) 0.3817 b) 0.6753 c) 0.7421 d) 0.8097 e) NOT

29. TFQ: It is not possible for the score in a distribution, not necessarily normal, which ranks as the 90th percentile to also be the median for the distribution.

30. TFQ: If 15 essays are submitted in a competition, there are 2730 ways in which the judges can award a first, second, and third prize.

31. MCQ: In a production run of 40 of a particular model of radiation detector, there are four which have defective circuits. If a sample of three of these is chosen without replacement, what is the probability that none of the three will be defective?

a) 0.5816 b) 0.6597 c) 0.7864 d) 0.9881 e) NOT

32. MCQ: If a gambler rolls two dice and gets a sum of 4 or 10, she wins $20. If she gets a sum of 7, she wins $10. It costs $5 to play the game. The expectation for this game is, to the nearest whole cent,

a) $0.42 b) -$0.28 c) -$0.72 d) $0.16 e) NOT

33. TFQ: If a distribution is bimodal, it is not possible for the median to be less than the smaller mode.

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#### Solution Summary

Probability and Statistics questins are answered.