Life of Smoke DetectorsThe average lifetime of smoke detectors that a company manufactures is5years, or60months,and the standard deviation is8 months.Find the probability that a random sample of32 smoke detectors will have a mean lifetime between58 and62 months.Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answer to at least four decimal places and intermediatez-value calculations to two decimal places.

P( 58 < x < 62) =