Question

9.	(15.24) The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for 6 randomly chosen women exceeds 270 days is about
	a 0.40. b 0.27. c 0.07.

10.

(15.12) The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.6 , but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.9 . 1. What is the mean (±0.1) of the average number of moths x¯¯¯x¯ in 50 traps? ____ 2. And the standard deviation of the average number of moths? (±0.001) ____ 3. Use the central limit theorem to approximate the probability (±0.01) that the average number of moths in 50 traps is greater than 0.6 : ____

11.

(15.28) Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.2. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 24. In answering the following, use z-scores rounded to two decimal places. If you choose one student at random, what is the probability (±±0.0001) that the student's score is between 20 and 30? ____ You sample 27 students. What is the standard deviation (±±0.01) of sampling distribution of their average score x¯¯¯x¯? ______ What is the probability (±±0.0001) that the mean score of your sample is between 20 and 30? _____

Answer 1