Hi, I need help solving part F. Thanks! Homework: 2-2 MyStatLab: Module Two Problem SetScore: 4.58 of 5 pts11 of 15 (15 complete)% 8.1.19-TSuppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u = 281 days and standard deviation o = 21 days. Complete parts (a) through (f) below.(a) What is the probability that a randomly selected pregnancy lasts less than 274 days?The probability that a randomly selected pregnancy lasts less than 274 days is approximately 0.3694 . (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 expectpregnancies to last exactly 274 days.O B. If 100 pregnant individuals were selected independently from this population, we would expectpregnancies to last more than 274 days.C. If 100 pregnant individuals were selected independently from this population, we would expect 37 pregnancies to last less than 274 days.(b) Suppose a random sample of 23 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.The sampling distribution of x isnormalwith= 281 and o; = 4.3788 .(Round to four decimal places as needed.)(c) What is the probability that a random sample of 23 pregnancies has a mean gestation period of 274 days or less?The probability that the mean of a random sample of 23 pregnancies is less than 274 days is approximately 0.0550 .(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.)A. If 100 independent random samples of size n= 23 pregnancies were obtained from this population, we would expectsample(s) to have a sample mean of 274 days or more.B. If 100 independent random samples of size n= 23 pregnancies were obtained from this population, we would expectsample(s) to have a sample mean of exactly 274 days.C. If 100 independent random samples of size n= 23 pregnancies were obtained from this population, we would expect 6 sample(s) to have a sample mean of 274 days or less.(d) What is the probability that a random sample of 50 pregnancies has a mean gestation period of 274 days or less?The probability that the mean of a random sample of 50 pregnancies is less than 274 days is approximately 0.0092.(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.)If 100 independent random samples of size n = 50 pregnancies were obtained from this population, we would expect 1 sample(s) to have a sample mean of 274 days or less.B. If 100 independent random samples of size n = 50 pregnancies were obtained from this population, we would expectsample(s) to have a sample mean of exactly 274 days.O C. If 100 independent random samples of size n= 50 pregnancies were obtained from this population, we would expectsample(s) to have a sample mean of 274 days or more.(e) What might you conclude if a random sample of 50 pregnancies resulted in a mean gestation period of 274 days or less?This result would be unusual, so the sample likely came from a population whose mean gestation period isless than281 days.(f) What is the probability a random sample of size 19 will have a mean gestation period within 9 days of the mean?The probability that a random sample of size 19 will have a mean gestation period within 9 days of the mean is(Round to four decimal places as needed.)

Name: Hi, I need help solving part F. Thanks! Homework: 2-2 MyStatLab: Modul
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Description: Hi, I need help solving part F. Thanks! Homework: 2-2 MyStatLab: Module Two Problem SetScore: 4.58 of 5 pts11 of 15 (15 complete)% 8.1.19-TSuppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u =

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Given Information:
μ=281 and σ=21
(f) To find the probability that a random sample of size 19 will…

(f) What is the probability a random sample of size 19 will have a mean gestation period within 9 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 9 days of the mean is (Round to four decimal places as needed.)