# HW3and4 - CLT(Central Limit Theorem and Normal...

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CLT(Central Limit Theorem) and Normal Probabilities - Draw a normal graph for each problem. Include x scores and z scores and shade appropriate areas. 1. Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. A) Find the probability that a randomly selected CD player will have a replacement time less than 8.0 years . B) If 45 CD players are randomly selected, how many of them would you expect to have a replacement time less than 8.0 years. C) Find the probability that 45 randomly selected CD players will have a mean replacement time greater than 7.0 years . 2. Assume that the weights of paper discarded by households each week are normally distributed with a mean of 9.4 lb and a standard deviation of 4.2 lb. A) Find the probability of randomly selecting a household and getting one that discards between 5.0 lb and 8.0 lb of paper in a week. B) If 16 households are randomly selected, find the probability that the mean amount of paper they discard in a week is more than 10.0 lb . 3. One classic use of the normal distribution is inspired by a letter to Dear Abby in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. A) Given this information, find the probability of a pregnancy lasting 308 days or longer . B) If 25 randomly selected women are put on a special diet just before they become pregnant, find the probability that their lengths of pregnancy have a mean that is less than 260 days (assuming that the diet has no affect - which means that the original data still applies). 4. Men spend an average of 11.4 min in the shower. Assume that the times are normally distributed with a standard deviation of 1.8 min. A) If 33 men are randomly selected, how many of them would you expect to spend at least 10.0 min in the shower? B) If 33 men are randomly selected, find the probability that their shower times have a mean between 11.0 and 12.0 minutes. 5. According to the International Mass Retail Association, girls aged 13 to 17 spend an average of \$31.20 on shopping trips in a month. Assume that the amounts are normally distributed with standard deviation of \$8.27. A)What percentage of girls in that age category spend between \$34.00 and \$40.00 in one month? B) If 85 girls in that age category are randomly selected, what is the probability that their mean monthly shopping expense is between \$30.00 and \$33.00? 6. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an organization for people with high IQs, and eligibility requires an IQ above 131.5 . A) What percentage of people meet the Mensa requirement? B) In a typical region of 75,000 people, how many are eligible for Mensa? C) If 25 people are randomly selected, what is the probability that the mean of their IQ's is above 105

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## This note was uploaded on 03/19/2011 for the course STAT 101 taught by Professor Hughes during the Spring '11 term at Andrews Univeristy.

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HW3and4 - CLT(Central Limit Theorem and Normal...

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