Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days x=247 days and standard deviation sigma equals days =13 days. Complete parts? (a) through? (f) below.

(a) What is the probability that a randomly selected pregnancy lasts less than 242 days?

The probability that a randomly selected pregnancy lasts less than 242 days is approximately nothing. 

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A. If 100 pregnant individuals were selected independently from this population, we would expect nothing pregnancies to last exactly 242 days.

B. If 100 pregnant individuals were selected independently from this population, we would expect nothing pregnancies to last less than 242 days.

C. If 100 pregnant individuals were selected independently from this population, we would expect nothing pregnancies to last more than 242 days.

(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of x overbarx is

Skewed Left Skewed right or Normal

with mu Subscript x overbar x equals=

nothing and sigma Subscript x overbar x equals=

(c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less?

The probability that the mean of a random sample of 17 pregnancies is less than 242 days is approximately nothing.

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.If 100 independent random samples of size n equals=17 pregnancies were obtained from this? population, we would expect nothing sample(s) to have a sample mean of 242 days or less.

B. If 100 independent random samples of size n equals=17 pregnancies were obtained from this? population, we would expect nothing ?sample(s) to have a sample mean of exactly 242 days.

C. If 100 independent random samples of size n equals=1717 pregnancies were obtained from this? population, we would expect nothing sample(s) to have a sample mean of 242 days or more.

d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less The probability that the mean of a random sample of 49 pregnancies is less than 242 days is approximately nothing.

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A. If 100 independent random samples of size n equals=4949 pregnancies were obtained from this population, we would expect nothing ?sample(s) to have a sample mean of exactly 242 days.

B. If 100 independent random samples of size n equals=49 pregnancies were obtained from this population, we would expect nothing ?sample(s) to have a sample mean of 242 days or less.

C. If 100 independent random samples of size n equals=49 pregnancies were obtained from this population, we would expect nothing sample(s) to have a sample mean of 242 days or more.

(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less

This result would be

expected, or unusual,

so the sample likely came from a population whose mean gestation period is

equal to less than or greater than 247 days.

(f) What is the probability a random sample of size 20 will have a mean gestation period within 11 days of the mean

The probability that a random sample of size 20 will have a mean gestation period within 11 days of the mean is

(Round to four decimal places as? needed.)