Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=251 days and standard deviation σ=18 days. Complete parts (a) through (f) below. (a) What is the probability that a randomly selected pregnancy lasts less than 245 days? The probability that a randomly selected pregnancy lasts less than 245 days is approximately 0.3696 (Round to four decimal places as needed.) 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 37 pregnancies to last less than 245 days. (b) Suppose a random sample of 22 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is normal with μx=251 and σx=3.8376 (Round to four decimal places as needed.) (c) What is the probability that a random sample of 22 pregnancies has a mean gestation period of 245 days or less? The probability that the mean of a random sample of 22 pregnancies is less than 245 days is approximately 0.0590 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=22 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 245 days. B. If 100 independent random samples of size n=22 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 245 days or more. C. If 100 independent random samples of size n=22 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 245 days or less.

          Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=251 days and standard deviation σ=18 days. Complete parts (a) through (f) below.
(a) What is the probability that a randomly selected pregnancy lasts less than 245 days?
The probability that a randomly selected pregnancy lasts less than 245 days is approximately 0.3696 (Round to four decimal places as needed.)
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 37 pregnancies to last less than 245 days.
(b) Suppose a random sample of 22 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
The sampling distribution of x is normal with μx=251 and σx=3.8376
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of 22 pregnancies has a mean gestation period of 245 days or less?
The probability that the mean of a random sample of 22 pregnancies is less than 245 days is approximately 0.0590
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=22 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of exactly 245 days.
B. If 100 independent random samples of size n=22 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 245 days or more.
C. If 100 independent random samples of size n=22 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 245 days or less.

Added by Aaron C.

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