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52. Which of the following distributions is described by the following example?
Many people can run a short distance of under two miles, but as the distance increases, fewer people can run that far.
53. The length of time to brush one’s teeth is generally thought to be exponentially distributed with a mean of $\frac{3}{4}$ minutes. Find the probability that a randomly selected person brushes his or her teeth less than $\frac{3}{4}$ minutes.
54. Which distribution accurately describes the following situation?
The chance that a teenage boy regularly gives his mother a kiss goodnight is about 20%. Fourteen teenage boys are randomly surveyed. Let
X = the number of teenage boys that regularly give their mother a kiss goodnight.
55. A 2008 report on technology use states that approximately 20% of U.S. households have never sent an e-mail. Suppose that we select a random sample of fourteen U.S. households. Let X = the number of households in a 2008 sample of 14 households that have never sent an email
Use the following information to answer the next three exercises: Suppose that a sample of 15 randomly chosen people were put on a special weight loss diet. The amount of weight lost, in pounds, follows an unknown distribution with mean equal to 12 pounds and standard deviation equal to three pounds. Assume that the distribution for the weight loss is normal.
56. To find the probability that the mean amount of weight lost by 15 people is no more than 14 pounds, the random variable should be:
57. Find the probability asked for in Question 56 .
58. Find the 90 ^{th} percentile for the mean amount of weight lost by 15 people.
Using the following information to answer the next three exercises: The time of occurrence of the first accident during rush-hour traffic at a major intersection is uniformly distributed between the three hour interval 4 p.m. to 7 p.m. Let X = the amount of time (hours) it takes for the first accident to occur.
59. What is the probability that the time of occurrence is within the first half-hour or the last hour of the period from 4 to 7 p.m.?
60. The 20 ^{th} percentile occurs after how many hours?
61. Assume Ramon has kept track of the times for the first accidents to occur for 40 different days. Let C = the total cumulative time. Then C follows which distribution?
62. Using the information in Question 61 , find the probability that the total time for all first accidents to occur is more than 43 hours.
Use the following information to answer the next two exercises: The length of time a parent must wait for his children to clean their rooms is uniformly distributed in the time interval from one to 15 days.
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