According to a study, the length of pregnancy of a randomly selected female has an unknown distribution with a mean of 272 days and a standard deviation of 14.1 days. Let XX be the length of pregnancy for a randomly selected female and let ¯¯¯XX¯  be the average length of pregnancy for a random sample of size 53. 1. Describe the probability distribution of XX and state its parameters μμ and σσ:  X∼X∼         ( μ=μ= , σ=σ= ) and find the probability that the length of pregnancy for a randomly selected female is between 239 and 285 days. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem       to describe the probability distribution of ¯¯¯XX¯ and state its parameters μ¯¯¯XμX¯ and σ¯¯¯XσX¯: (Round the answers to 1 decimal place)  ¯¯¯X∼X¯∼         ( μ¯¯¯X=μX¯= , σ¯¯¯X=σX¯= ) and find the probability that the average length of pregnancy for a sample of 53 randomly selected females is less than 272 days. (Round the answer to 4 decimal places)

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