Question

t, Inc. produces AA batteries used in remote-controlled toy cars. The mean l ife of these batterles follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power Inc. tests samples of 25 batterles. a. What can you say about the shape of the distributi of the sample mean? b. What is the standard error of the distribution of the sample mean? (Round your answer to 1 decimal places.) c. What proportion of the samples will have a mean useful life of more than 36 hours? (Round your z value to 2 decimal places and final answer to 4 decimal places.) < Prey 2of8 Next >

Answer 1

Given that mean(mu) = 35, s.p(sigma) = 5.5, n = 25 Normal sigma_x^bar = sigma/squareroot n = 5.5/squareroot 25 = 1.1 P(x^bar > 36) = P(z > 36-35/5.5/squareroot 25) = P(z < 0.9091) = P(z > 0.91) = 0.1814 P(x^bar > 34.5) = P(z > 34.5-35/5.5/squareroot 25) = P(z > -0.45) = 0.6736 P(34.5 < x^bar z < 36) = P(34.5-35/1.1 < z < 36-35/1.1) = P(-0.45 < z < 0.91) = P(z < 0.91)-P(z < -0.45) = 0.8186-0.3264 = 0.4922