Question

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

mean μ equals 266

and standard deviation sigma equals 27 days

What is the probability that a random sample of 18 pregnancies has a mean gestation period of 257 days or less? The probability that the mean of a random sample of 18 pregnancies is less than 257 days is approximately The probability that the mean of a random sample of 18 pregnancies is less than 257 days is approximately 0.0793. (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 =18 pregnancies were obtained from this population, we would expect ?? sample(s) to have a sample mean of 257 days or less. B. If 100 independent random samples of size n=18 pregnancies were obtained from this population, we would expect ?? sample(s) to have a sample mean of exactly 257 days. C. If 100 independent random samples of size n=18 pregnancies were obtained from this population, we would expect ?? sample(s) to have a sample mean of 257 days or more. Select the correct choice below and fill in the answer box within your choice

Answer 1

a) P(X < 257)

= P((X -a) P(X < 257)

= P((X - μ/ σ ) < P ( 257 - μ/ σ)

= P(Z < (257 - 266)/27)

= P(Z < -0.33)

= 0.3707

Expected value = 100 * 0.3707 = 37.07 = 37

Option - A) If 100 pregnant individuals were selected independently from this population, we would expect 37 pregnancies to last less than 257 days.