STATISTICS FOR DECISION MAKING Dr. Azar Abizada HOMEWORK 3 Due Date: Wednesday, February 25th class time Question 1. When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean 92 and a standard deviation 3.6. A random sample of 4 different hours was taken. a. b. c. d. e. f. g. What is the probability that the sample mean exceeds 93? What is the probability that the sample mean is between 89 and 91? What is the probability that the sample mean is between 93 and 95? What is the probability that the sample mean is either above 94 or below 90? The probability is 0.7 that the sample mean is below what value? The probability is 0.4 that the sample mean is above what value? What is the probability that the sample mean is both below 96 and above 89? Question 2. A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders. Suppose that this belief is correct. A random sample of 144 current stockholders is taken. a. If random sample of 144 current stockholders is taken, what is the probability that more than 15% of them will find offer teams attractive? b. If random sample of 100 current stockholders is taken, what is the probability that less than 24% of them will find offer teams attractive? c. If random sample of 81 current stockholders is taken, what is the probability that less than 74% of them will not find offer teams attractive? d. If random sample of 100 current stockholders is taken, what is the probability that more than 60% of them will not find offer teams attractive? e. If random sample of 121 current stockholders is taken, what is the probability that 23% to 26% of these stockholders will find offer teams attractive? Question 3: Suppose that the US Centers for Disease Control and Prevention (CDC) believe that influenza activity will be lower than the same period last year. Residents in the Atlanta metropolitan area were asked if this news by the CDC would persuade them not to take the flu vaccine. If only 40 people from a random sample of 246 stated that they now would not take the flu vaccine, a) Estimate with 98% confidence the proportion of all residents in the Atlanta metro area who now consider the flu vaccine necessary. b) Estimate with 94% confidence the proportion of all residents in the Atlanta metro area who now consider the flu vaccine necessary. Question 4. It has been found that times taken by people to complete a particular tax form follow a normal distribution with mean 100 minutes and standard deviation 30 minutes. A random sample of nine people who have completed this tax form was taken. a) What is the probability that the sample mean time taken is between 110 and 120 minutes? b) What is the probability that the sample mean time taken is more than 115 minutes? c) The probability is .20 that the sample mean time taken is less than how many minutes? d) The probability is .30 that the sample mean time taken is more than how many minutes? Question 5: A college admissions officer for an M.B.A. program has determined that historically applicants have undergraduate grade point averages that are normally distributed with standard deviation 0.45. From a random sample of 25 applications from the current year, the sample mean grade point average is 2.90. a) Find a 96% confidence interval for the population mean. b) Based on the sample results, a statistician computes for the population mean a confidence interval extending from 2.81 to 2.99. Find the confidence level associated with this interval. Question 6: Annual sales revenue for Meadow Flower Cereal is $500,000.000. Jeffery Shower, a 52 year old senior vice president, is in charge of production and sales of Nutty 8 cereal. Daily production in cases is normally distributed with a mean of 100 and a variance of 625. Daily sales in cases are also normally distributed with a mean of 100 and standard deviation of 8. Sales and production have a correlation of 0.60. The selling price per case is $10. The variable production cost per case is $7. The fixed production costs per day are $250. What is the probability that total revenue is greater than total costs on any day