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 = 116 days and standard deviation sigma = 8 days. (a) What is the probability that a randomly selected pregnancy lasts less than 113 days? The probability that a randomly selected pregnancy lasts less than 113 days is approximately 3520. (Round to four decimal places as needed.) (b) What is the probability that a random sample of 12 pregnancies has a mean gestation period of 113 days or less? The probability that the mean of a a random sample of 12 pregnancies is less than 113 days is approximately 0970 (Round to four decimal places as needed.) (c) What is the probability that a random sample of 36 pregnancies has a mean gestation period of 113 days or less? The probability that the mean of a a random sample of 36 pregnancies is less than 113 days is approximately (Round to four decimal places as needed.)

Explanation / Answer

mean = 116
std. dev. = 8

(a)
P(x < 113) = P(z < (113 - 116)/8) = P(z < -0.375) = 0.3538

Hence required probability = 0.3538

(b)
P(x < 113) = P(z < (113 - 116)/(8/sqrt(12))) = P(z < -1.299) = 0.0970

Hence required probability = 0.0970

(c)
P(x < 113) = P(z < (113 - 116)/(8/sqrt(36))) = P(z < -2.25) = 0.0122

Hence required probability = 0.0122

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