44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between $3.78 and $3.86? c. What is the probability that the difference between the sample mean and the popu-lation mean is less than $0.01? d. What is the likelihood the sample mean is greater than $3.92?

56. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premi-ums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000. a. Based on this sample information, develop a 90% confidence interval for the popula-tion mean yearly premium. b. How large a sample is needed to find the population mean within $250 at 99% confidence?

66. Near the time of an election, a cable news service performs an opinion poll of 1,000 prob-able voters. It shows that the Republican contender has an advantage of 52% to 48%. a. Develop a 95% confidence interval for the proportion favoring the Republican candidate. b. Estimate the probability that the Democratic candidate is actually leading. c. Repeat the above analysis based on a sample of 3,000 probable voters.

71. Refer to the Lincolnville School District bus data. a. Develop a 95% confidence interval for the mean bus maintenance cost. b. Develop a 95% confidence interval for the mean bus odometer miles. c. make abusiness memo to the state transportation official to report your results.

Century National BankRefer to the description of Century National Bank at the end of the Review of Chapters 1-4 on page 129. When Mr. Selig took over as president of Century several years ago, the use of debit cards was just beginning. He would like an update on the use of these cards. Develop a 95% confi-dence interval for the proportion of customers using these cards. On the basis of the confidence interval, is it reason-able to conclude that more than half of the customers use a debit card? Make abrief report interpreting the results.

Data Set 3 --Lincolnville School District Bus Data Engine Type Maintenance Odometer ID Manufacturer (0=diesel) Capacity Cost Age Miles 4646 54375 Thompson 1072 21858 122 Bluebird 9394 1.16580 751 1078 22444 279 Bluebird 1008 22672 Bluebird 5329 50765 520 Bluebird 4794 1 19130 37872 714 Bluebird 3742 73703 875 Bluebird 4376 97947 500 Bluebird 4832 119860 Bluebird 5160 1.17760 Bluebird 195 Bluebird 2775 Bluebird 69438 365 Keiser 3065 63384 162 keiser 8143 31266 586 Bluebird 1569 34674 370 7766 36528 887 Bluebird 3743 93672 164 Bluebird 2540 34530 948 Keiser 1342 97956 678 keiser 3361 75229 181 3097 34362 Bluebird 8263 102969 Bluebird 1218 83424 Bluebird 2028 40824 Bluebird Bluebird 9069 98307 Bluebird 71970 Keiser 9193 101889 4795 106605 Bluebird 505 10276 Bluebird 2732 70122 724 3754 32 keiser 4640 196 880 ser 8410 65\f