B3. Two companies A and B produce batteries. Batteries from company A have an expected lifetime of μA = = 2 9 hours with a standard deviation of σA hours. Batteries from company B have an expected lifetime of μB = 10 hours with a standard deviation of бв σB = 1 hour. (a) Let X1, ..., ✗, be the lifetimes of n n randomly chosen batteries from company A. What is the approximate distribution of the average lifetime ✗, n - Η ΣΧ? n (b) Independent of the batteries already chosen, n randomly chosen batteries from company B are selected. Let Y₁,..., Y be the n corresponding lifetimes, and let 'n Yn = 1½ Y; be the average lifetime. What n i=1 is the approximate distribution of ✗n - Yn? (c) Approximately how large a sample n should be chosen to ensure that P(X < Yn) ≥ 0.999? (It may be useful to know that, for a standard normal distribution, we have (3.09) = 0.999.)

A scientist is studying the paramecium, a one-celled organism, under a microscope. There are 1500 paramecia in the slide he is studying, and the standard deviation of their lengths is 0.12mm. He views a sample of 30 paramecia and finds that the mean length of these 30 specimens is 0.25mm. Give the point estimate of the mean length of the entire paramecium population in the slide? (a) (b) Construct a 95% confidence interval for the mean length of the population. (c) State the maximum error for the estimate?

A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. You decide to measure battery lifetime by recording the time it takes for the battery charge to run out while a tester is streaming videos on the phones continuously. Then you select a random sample of 45 cell phones of the manufacturer's latest model and record their battery lifetimes. Assume that the population standard deviation of the battery lifetimes for that cell phone model (using your method of measurement) is 2.42 hours. Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 45 phones of the manufacturer's latest model. Take Sample Sample size: 0 Number of phones Point estimate: 0 45 Sample mean…

A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. You decide to measure battery lifetime by recording the time it takes for the battery charge to run out while a tester is streaming videos on the phones continuously. Then you select a random sample of 45 cell phones of the manufacturer's latest model and record their battery lifetimes. Assume that the population standard deviation of the battery lifetimes for that cell phone model (using your method of measurement) is 2.42 hours. Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 45 phones of the manufacturer's latest model. Take Sample Sample size: Number of phones Point estimate: 45 Sample mean Standard…