Suppose the lengths of the pregnancies of a certain animal areapproximately normally distributed with mean mu equals 127 days andstandard deviation sigma equals 12 days. Complete parts​ (a)through​ (f) below. ​(a) What is the probability that a randomlyselected pregnancy lasts less than 123 ​days? The probability thata randomly selected pregnancy lasts less than 123 days isapproximately 0.3694. ​(Round to four decimal places as​ needed.)Interpret this probability. Select the correct choice below andfill in the answer box within your choice. ​(Round to the nearestinteger as​ needed.) A. If 100 pregnant individuals were selectedindependently from this​ population, we would expect 37 pregnanciesto last less than 123 days. B. If 100 pregnant individuals wereselected independently from this​ population, we would expectnothing pregnancies to last more than 123 days. C. If 100 pregnantindividuals were selected independently from this​ population, wewould expect nothing pregnancies to last exactly 123 days. ​(b)Suppose a random sample of 20 pregnancies is obtained. Describe thesampling distribution of the sample mean length of pregnancies. Thesampling distribution of x overbar is normal with mu Subscript xoverbarequals 127 and sigma Subscript x overbarequals 2.9104.​(Round to four decimal places as​ needed.) ​(c) What is theprobability that a random sample of 20 pregnancies has a meangestation period of 123 days or​ less? The probability that themean of a random sample of 20 pregnancies is less than 123 days isapproximately nothing. ​(Round to four decimal places as​ needed.)Interpret this probability. Select the correct choice below andfill in the answer box within your choice. ​(Round to the nearestinteger as​ needed.) A. If 100 independent random samples of sizenequals20 pregnancies were obtained from this​ population, we wouldexpect nothing ​sample(s) to have a sample mean of 123 days orless. B. If 100 independent random samples of size nequals20pregnancies were obtained from this​ population, we would expectnothing ​sample(s) to have a sample mean of 123 days or more. C. If100 independent random samples of size nequals20 pregnancies wereobtained from this​ population, we would expect nothing ​sample(s)to have a sample mean of exactly 123 days. ​(d) What is theprobability that a random sample of 39 pregnancies has a meangestation period of 123 days or​ less? The probability that themean of a random sample of 39 pregnancies is less than 123 days isapproximately nothing. ​(Round to four decimal places as​ needed.)Interpret this probability. Select the correct choice below andfill in the answer box within your choice. ​(Round to the nearestinteger as​ needed.) A. If 100 independent random samples of sizenequals39 pregnancies were obtained from this​ population, we wouldexpect nothing ​sample(s) to have a sample mean of 123 days orless. B. If 100 independent random samples of size nequals39pregnancies were obtained from this​ population, we would expectnothing ​sample(s) to have a sample mean of exactly 123 days. C. If100 independent random samples of size nequals39 pregnancies wereobtained from this​ population, we would expect nothing ​sample(s)to have a sample mean of 123 days or more. ​(e) What might youconclude if a random sample of 39 pregnancies resulted in a meangestation period of 123 days or​ less? This result would be ▼expected, unusual, so the sample likely came from a populationwhose mean gestation period is ▼ less than equal to greater than127 days. ​(f) What is the probability a random sample of size 15will have a mean gestation period within 12 days of the​ mean? Theprobability that a random sample of size 15 will have a meangestation period within 12 days of the mean is nothing. ​(Round tofour decimal places as​ needed.)