Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean 228 days and standard deviation g = 20 days. Complete parts (a) through (f) below. (a) What is the probability that a randomly selected pregnancy lasts less than 221 days? The probability that a randomly selected pregnancy lasts less than 221 days is approximately (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.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 221 days. OB. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last less than 221 days. O C. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 221 days (b) Suppose a random sample of 20 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies The sampling distribution of xis (1) - (Round to four decimal places as needed.) - with = and o: -

Answer 1

al alls nolmally a consider, Anse. Given that, a certain pregnancies of Lengthe of noch all animal dessibuted with mean, l = 228 days and standard denation, s=20 days Probability that a randomly selected pregnancy laste less than 224 days = P(x2221) = ? P(xc221) = (x - 4. 221-228 ) = 8(26 -0.35) from the standard Normal Table, we get plz<^0-35) 20.3632 P(xcazi) 0.3632 / 221- 228 20 = 0.3632 P(xc221) 2 0.3632 = 36.327 367. I. Interpretation - It too pregnant individuals were selected individually independentley from the population, we would expect (36 pregnencies to last less than 21 days d. option ③ es correct

6 a Given that when 20 sample pregnencies are obtained then the sampling distributions of Normal Distribution with him = la 228 and 2012 4.4721 221-228. 4.4721 ① low consider for sample of so pregnenetes, Probability that mean gestation period of 221 days or less - P(x <221) = ? plã <221) - Pla de 2012) = P(za 1.57) from the standard Normal Table, we get P (za 1.57) - 0.0588 pã (225) = 0.0588 0.0588

Interpretatios:- Plä 2221) - 0.0888 = 5.88 4. & 67 If 100 independent random samples of size, n=20 pregnancies well obtained from this population we would expect 6 Sample (6) to have a sample mean. of 221 days or less. de option © Es correct @ now conside for 40 samples, la= l = 228 and och 31623 ? o = 3.1623 Now consider Probability the mean of this Sample is less than 221 deer = P(x <221) = ? 221 - 228 PER 22351) - deste 1933 3.1623

Pluk 221) = Plze - 22-1361) Plac– 22.14) from the standard Normal Tables we P(Zc-22-14) 2 gaty 0.0124 p(7 (221) = 0.0134 Interpretation : PCT 6221) = 0.0134 = 1.34.). V it If 100 independent rondom samples of size, no 40 pregnanuis were obtained from the populations, we would expect I Sample to have a sample mean of 20 days or less i option © es correct

@ a hele Conclusion from past & - Here plz c22)= (... The result So the sample likely come from mean gestation es greater than would be uncenal a population whose 28 days € Given Sample size, n=19. lal z228 & Home D 20 = 4.5883 Consider Probability that mean & wither & days a p(x(8) = ? PLE <s). Pl_la_5379) Table, we get from = P(Z <-49-95) the standard Normal P(Z <-4720 = 0.0000