having trouble answering part C. Please show work if possible. thank You!!!!

Homework: Section 8.1 Homework Save Score: 0.08 of 1 pt 5 of 12 (12 complete) HW Score: 79.84%, 9.58 of 12 pts 8.1.19-T Question Help Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u = 127 days and standard deviation o = 12 days. Complete parts (a) through (f) below. (a) What is the probability that a randomly selected pregnancy lasts less than 123 days? The probability that a randomly selected pregnancy lasts less than 123 days is approximately 0.3707 . (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 123 days. B. If 100 pregnant individuals were selected independently from this population, we would expect 37 pregnancies to last less than 123 days. O C. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 123 days. (b) Suppose a random sample of 24 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is normal with u- = 127 and of = 2.4495 . (Round to four decimal places as needed.) (c) What is the probability that a random sample of 24 pregnancies has a mean gestation period of 123 days or less? The probability that the mean of a random sample of 24 pregnancies is less than 123 days is approximately. (Round to four decimal places as needed.)