Mathematics

Complete the problems below from the textbook. You will need to use the “Baseball 2012 Data,” “Buena School District Bus Data,” and the “Century National Bank Data” files for this assignment.

- Chapter 6 – Problem 45
- Chapter 6 – Problem 71
- Chapter 7 – Problem 53
- Chapter 7 – Problem 55
- Chapter 7 – Problem 76
- Chapter 7 Case A – Century National Bank

For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output. This information is needed in order to receive full credit on these problems.

Submit output in one Excel file.

45. An auditor for Health Maintenance Services of Georgia reports 40% of policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records. a. How many of the policyholders would you expect to have filed a claim within the last year? b. What is the probability that 10 of the selected policyholders submitted a claim last year? c. What is the probability that 10 or more of the selected policyholders submitted a claim last year? d. What is the probability that more than 10 of the selected policyholders submitted a claim last year?

71. Refer to the Baseball 2012 data. Compute the mean number of home runs per game. To do this, first find the mean number of home runs per team for 2012. Next, divide this value by 162 (a season comprises 162 games). Then multiply by 2 because there are two teams in each game. Use the Poisson distribution to estimate the number of home runs that will be hit in a game. Find the probability that: a. There are no home runs in a game. b. There are two home runs in a game. c. There are at least four home runs in a game.

53. Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate weekly production follows the normal distribution. The mean of this distribution is 4,000 units per week and the standard deviation is 60 units per week. If the bonus is paid on the upper 5% of production, the bonus will be paid on how many units or more?

55. Best Electronics Inc. offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day.a. In what percent of the days are there eight or fewer customers returning items?b. In what percent of the days are between 12 and 14 customers returning items?c. Is there any chance of a day with no returns?

76. Refer to the Buena School District bus data. a. Refer to the maintenance cost variable. The mean maintenance cost for last year is $450.29, with a standard deviation of $53.69. Estimate the number of buses with a cost of more than $500. Compare that with the actual number. b. Refer to the variable on the number of miles driven. The mean is 830.11 and the standard deviation is 42.19 miles. Estimate the number of buses traveling more than 900 miles. Compare that number with the actual value.

A. Century National BankRefer to the Century National Bank data. Is it reasonable that the distribution of checking account balances approxi-mates a normal probability distribution? Determine the mean and the standard deviation for the sample of 60 cus-tomers. Compare the actual distribution with the theoretical distribution. Cite some specific examples and comment on your findings. Divide the account balances into three groups, of about 20 each, with the smallest third of the balances in the first group, the middle third in the second group, and those with the largest balances in the third group. Next, develop a table that shows the number in each of the categories of the account balances by branch. Does it appear that account balances are related to the branch? Cite some examples and comment on your findings.

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