Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 263 days and standard deviation sigma equals 15 days. Complete parts​ (a) through​ (f) below. ​(a) What is the probability that a randomly selected pregnancy lasts less than 257 ​days? The probability that a randomly selected pregnancy lasts less than 257 days is approximately nothing. ​(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 pregnant individuals were selected independently from this​ population, we would expect nothing pregnancies to last less than 257 days. B. If 100 pregnant individuals were selected independently from this​ population, we would expect nothing pregnancies to last more than 257 days. C. If 100 pregnant individuals were selected independently from this​ population, we would expect nothing pregnancies to last exactly 257 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 overbar is ▼ normal skewed left skewed right with mu Subscript x overbarequals nothing and sigma Subscript x overbarequals nothing. ​(Round to four decimal places as​ needed.) ​(c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 257 days or​ less? The probability that the mean of a random sample of 17 pregnancies is less than 257 days is approximately nothing. ​(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 nequals17 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of exactly 257 days. B. If 100 independent random samples of size nequals17 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 257 days or less. C. If 100 independent random samples of size nequals17 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 257 days or more. ​(d) What is the probability that a random sample of 37 pregnancies has a mean gestation period of 257 days or​ less? The probability that the mean of a random sample of 37 pregnancies is less than 257 days is approximately nothing. ​(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 nequals37 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 257 days or less. B. If 100 independent random samples of size nequals37 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 257 days or more. C. If 100 independent random samples of size nequals37 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of exactly 257 days. ​(e) What might you conclude if a random sample of 37 pregnancies resulted in a mean gestation period of 257 days or​ less? This result would be ▼ expected, unusual, so the sample likely came from a population whose mean gestation period is ▼ greater than less than equal to 263 days. ​(f) What is the probability a random sample of size 15 will have a mean gestation period within 11 days of the​ mean? The probability that a random sample of size 15 will have a mean gestation period within 11 days of the mean is nothing. ​(Round to four decimal places as​ needed.)

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Answer 1