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Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean...

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 190 days and standard deviation sigma equals 14 days

Complete parts​ (a) through​ (f) below.

​(a) What is the probability that a randomly selected pregnancy lasts less than 185 ​days?

​(b) Suppose a random sample of 20 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

c) What is the probability that a random sample of 20 pregnancies has a mean gestation period of 146 days or​ less?

(d) What is the probability that a random sample of 42 pregnancies has a mean gestation period of 146 days or​ less?

​(e) What might you conclude if a random sample of 42 pregnancies resulted in a mean gestation period of 146 days or​ less?

(f) What is the probability a random sample of size 8 will have a mean gestation period within 13 days of the​ mean?

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