Question

Problem 4 The length of maternity stay in U.S. hospitals is normally distributed, with mean of 2.6 days and a standard deviation of 0.5 days. We randomly survey 89 women who recently bore children in U.S. hospitals. Let X = maternity stay in U.S. hospital, and X = average maternity stay for a sample of size 89 a. X (pick one) ) b. X (pick one) . с. What is the probability that the average stay is more than 3 days? PX > 3) = d. Which of the following is more likely? an individual stays more than 5 days the average stay of 89 women was more than 5 days

Answer 1

From CLT, X NN (nu, n2o2) i.e. N (89x2.6 58 92 00:52) 1. eN/23).4 44.5) dist DFNN (U,/vn) TeN(Q:6, 0.053) O P 1% >3) = P(Z > 3-26 =P(2>7-55) - 1-P (z 30.755) = 0.0000 Ans :6) 0.053

d) Average stay of women is more than 5 days is more likely since mean stay is 231.4 with SD of 44.5 so Probability of stay greater than 5 is very likely.