Question

8.1.19 Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean u 212 days and standard deviation a 13 days. Complete parts (a) through () below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2), (a) What is the probability that a randomly selected pregnancy lasts less than 207 days? The probability that a randomly selected pregnancy lasts less than 207 days is approximately 0.3520. (Round to four decimal places as needed.) Interpret this probability. Select thetcorrect 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 wouid expect 35 pregnancies to last less than 207 days. B. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 207 days. OC. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 207 days. (b) Suppose a random sample of 19 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is normal 212 and a; 2.9824 with (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 207 days or less? The probability that the mean of a random sample of 19 pregnancies is less than 207 days is approximately 0.0465. (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.) 19 pregnancies were obtained from this population,, we would expect 5 sample(s) to have a sample mean of 207 days or less. OA If 100 independent random samples of size n sample(s) to have a sample mean of 207 days or more. O B. 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 exactly 207 days. 19 pregnancies were obtained from this population, we would expect C. If 100 independent random samples of size n (d) What is the probability that a random sample of 41 pregnancies has a mean gestation period of 207 days or less? The probability that the mean of a random sample of 41 pregnancies is less than 207 days is approximately 0.0069 (Round to four decimal places as needed.) Question is complete. Tap on the red indicators to see incorrect answers. All narts showing

I need help. PLEASE DONT USE THE STANDARD NORMAL DISTRIBUTION TABLE. use normalcdf as part of your answer.

Thank you

Answer 1

Let X be a that donate random variable prognncies longths of 13 Where, Znaco, XwHormal ( 212, 132) P ( x < 207) - P ( x - 212 & 207-212) = P(24 os) = € (-5 fo.35026 If 100 prognont individiuds were this bobulation, we would expect 35 less than 200 days. net XIN Normal (212, 432) A from last selected independently pregnancies to .. tror ELZ): ver (f) - & Th. Exi sex - 212 varlty) a var (x ) = 132 = 8.8942 7. NC212, 8- 8907) 2 PC P 07) -212 18.89472 8543 d) - & (7 & 207) PC Fair 212 = -5 VIE ) = (- Stra) -0.006g)