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

Question

Suppose the lengths of the pregnancies of a certain animal arc approximately normally distributed with mean mu - 282 days and standard deviation sigma = 26 days. Complete parts (a) through (c). (a)What is the probability that a randomly selected pregnancy lasts less than 272 days? The probability that a randomly selected pregnancy lasts less than 272 days is approximately. (b)What is the probability that a random sample of 15 pregnancies has a mean gestation period of less than 272 days? The probability that the mean of a random sample of 15 pregnancies is less than 272 days is approximately. (c) What is the probability that a sample of 30 pregnancies has a mean gestation period of less than 272 days? The probability that the mean of a random sample of 30 pregnancies is less than 272 days is approximately .

Explanation / Answer

z=( 272-282)/26=-0.38

P( x <272) = P( z < -0.38) = 0.3520

z=( 272-282)/(26/sqrt(15))= -1.49

P( mean x <272) = P( z < -1.49) = 0.0681

z=( 272-282)/(26/sqrt(30))= -2.11

P( mean x <272) = P( z < -2.11) = 0.0174

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