Suppose the lengths of the pregnancies of a certain animal are approximately nor

Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 241 days and standard deviation sigma equals 15 days . (a) What is the probability that a randomly selected pregnancy lasts less than 236 days? The probability that a randomly selected pregnancy lasts less than 236 days is approximately 0.3707 . (Round to four decimal places as needed.) (b) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 236 days or less? The probability that the mean of a a random sample of 18 pregnancies is less than 236 days is approximately 0.0793 . (Round to four decimal places as needed.) (c) What is the probability that a random sample of 59 pregnancies has a mean gestation period of 236 days or less? The probability that the mean of a a random sample of 59 pregnancies is less than 236 days is approximately 0.0052 . (Round to four decimal places as needed.)

Explanation / Answer

a) z = (236 - 241)/15

z = - 0.33

P = 0.3707

b) z = (236 - 241)/15/18

z = - 1.41

P = 0.0793

c) z = (236 - 241)/15/59

z = - 2.56

P = 0.0052

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