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Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ = 266 days and standard deviation a = 20 days. Complete parts (a) through (f) below.
I
The probability that a randomly selected pregnancy lasts less than 260 days is approximately 0.3821. (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.)
OA. If 100 pregnant individuals were selected independently from this population, we would expect
pregnancies to last more than 260 days.
B.
If 100 pregnant individuals were selected independently from this population, we would expect 38 pregnancies to last less than 260 days.
OC. If 100 pregnant individuals were selected independently from this population, we would expect preghancies to last exactly 260 days.
(b) Suppose a random sample of 19 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
normal with P = 266 and 5 = 4.5883
The sampling distribution of x is
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of 19 pregnancies has a mean gestation period of 260 days or less?
The probability that the mean of a random sample of 19 pregnancies is less than 260 days is approximately 0.0955
(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 = 19 pregnancies were obtained from this population, we would expect 10 sample(s) to have a sample mean of 260 days or less.
OB. If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect
OC. If 100 independent random samples of size n = 19 pregnancies were obtained from this population, we would expect
sample(s) to have a sample mean of 260 days or more.
sample(s) to have a sample mean of exactly 260 days.
(d) What is the probability that a random sample of 57 pregnancies has a mean gestation period of 260 days or less?
The probability that the mean of a random sample of 57 pregnancies is less than 260 days is approximately
(Round to four decimal places as needed.).