The Central Limit Theorem for Sample Means (Averages) Use the foiiowing information to answer the next six exercises: Yoonie is a personnel man ager in a large corporation. Each month she must review 16 of the employees. From past ex perience, she has found that the reviews ta ke her approximately four hours each to do with a population standard deviation of 1.2 hours. LetX be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let? be the ran dom variable representing the mean time to complete the 16 reviews. Assume that the 16 re views represent a random set of reviews. 1. What is the mean. standard deviation, and sample size? 2. Complete the distributions. X N ( lJ X "' l . J 3. Find the probability that one review will take Yoonie from 3.6 to 4.26 hours. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability. Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 6.8 ft and standard deviation 53.6 ft. You intend to measure a random sample of n = 212 trees. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error (standard deviation) of the sampling distribution. Complete the indicated boxes, correct to two decimal places. Hi 6.8 Of = 6.8 Submit QuestionScore: ossrs Hg answered Progress saved Done a 115' Fl. 1! Question 3 v E on pt '0 2 3 99 (0 Detail A population of values has a normal distribution with p. = 6.9 and or = 43.5. You intend to draw a random sample of size n. = 81. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means [i.e. the standard error}? [Report answer accurate to 2 decimal places} Score. 0.35/9 answered Progress saved Done VO . . . . Question 4 0/1 pt O 2 99 0 Detail Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 94 ft and standard deviation 78.6 ft. You intend to measure a random sample of n = 80 trees. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places. Hi = Submit QuestionInjune 2005, a survey was conducted in which a random sample of 1,464 U.S. adults was asked the following question: "In 1973 the Roe versus Wade decision established a woman's constitutional right to an abortion, at least in the rst three months of pregnancy. Would you like to see the Supreme Court completely overturn its Roe versus Wade decision, or not?" The results were: Yes30%, No63%, Unsure?% (Source: vwvw.Pollingreport.com} Which ofthe following is true? 0 {A}: 30%, 63%, and 7% are all parameters. 0 [B]: 30%, 63%, and ?% are all statistics. 0 {C}: Ifanother random sample of size 1,464 U.S. adults were to be chosen, we would expect to get the exact same distribution of answers. 0 Both [A] and {C} are correct. 0 Both {B} and {C} are correct. Submit
