The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 9 months. Find the probability that a random sample of 31 smoke detectors will have a mean lifetime between 57 and 62 months. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answer to four decimal places and intermediate : value calculations to two decimal places. P (57 < X < 62) = ___