The length of human pregnancies is approximately normal with mean p. = 266 days and standard deviation 5 =16 days. Complete parts (a} through (f). (a) What is the probability that a randomly selected pregnancy lasts less than 260 days? The probability that a randomly selected pregnancy lasts less than 260 days is approximately (Round to tour 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.) Q A- It 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last less than 260 days. Cl 3- If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 260 days. Cl C- It 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 260 days. (b) Suppose a random sample of 17 human pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of it is V with p; = and Oi = (Type integers or decimals rounded to four decimal places as needed.) (c) What is the probability that a random sample of 17' pregnancies has a mean gestation period of 260 days or less? The probability that the mean of a random sample of 17 pregnancies is less than 260 days is approximately (Round to four decimal places as needed.) (c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 260 days or less? The probability that the mean of a random sample of 17 pregnancies is less than 260 days is approximately (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.) '33::3' A- If 100 independent random samples of size n = 17 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 260 days. Cl 3- If 100 independent random samples of size n = 17 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 260 days or more. '3' C- If 100 independent random samples of size n = 17 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 260 days or less. (d) What is the probability that a random sample of 46 pregnancies has a mean gestation period of 260 days or less? The probability that the mean of a random sample of 46 pregnancies is less than 260 days is approximately (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 independent random samples of size n = 46 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 260 days or more. O B. If 100 independent random samples of size n = 46 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 260 days. O C. If 100 independent random samples of size n = 46 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 260 days or less.(e) What might you conclude if a random sample of 46 pregnancies resulted in a mean gestation period of 260 days or less? This result would be so the sample likely came from a population whose mean gestation period is 266 days. (f) What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean? The probability that a random sample of size 15 will have a mean gestation period within 10 days of the mean is (Round to four decimal places as needed.)