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The Sony Corporation produces a Walkman that requires two AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribtion of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of their testing program Sony tests samples of 25 batteries. (a) What can you say about the shape of the distribution of sample mean? (b) What is the standard error of the distribution of the sample mean? (c) What proportion of the samples will have a mean useful life of more than 36 hours? (d) What proportion of the sample will have a mean useful life greater than 34.5 hours? (e) What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours? In the answer can you show how you came up with the conifidence limits and proportions (a) (b) (c) (d) (e) The shape of distribution is normal distribution. Standard error = Standard deviation/ (n)1/2 = 5.5/ (25)1/2 = 1.1 Z = Value – Mean / std dev = 36 – 35 / 5.5 = .1818 Probability = 42.86% Z = Value – Mean / std dev = 34.5 – 35 / 5.5 = -.09 Probability = 53.59% proportion of the sample will have a mean useful life between 34.5 and 36.0 hours = 100 – proportion having less than 34.5 - proportion having more than 36 = 100 – (100-53.59) – 42.86 = 10.73%

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