# 6.2 x is uniformly distributed over a range of values from 8 to 21....

## Question

6.2 x is uniformly distributed over a range of values from 8 to 21.
a. What is the value of f(x) for this distribution?
b. Determine the mean and standard deviation of this distribution.
C. Probability of (10 ≤x<17)=?
d. Probability of (x < 22) = ?
e. Probability of (x ≥ 7)?

6.10 Toolworkers are subject to work-related injuries. One disorder, caused by strains to the hands and wrists, is called carpal tunnel syndrome. It strikes as many as 23,000 workers per year. The U.S. Labor Department estimates that the average cost of this disorder to employers and insurers is approximately \$30,000 per injured worker.
Suppose these costs are normally distributed, with a standard deviation of \$9,000.
a. What proportion of the costs are between \$15,000 and \$45,000?
b. What proportion of the costs are greater than \$50,000?
c. What proportion of the costs are between \$5,000 and \$20,000?
d. Suppose the standard deviation is unknown, but 90.82% of the costs are more than \$7,000. What would be the value of the standard deviation?
e. Suppose the mean value is unknown, but the standard deviation is still \$9,000. How much would the average cost be if 79.95% of the costs were less than \$33,000?

6.20 The Zimmerman Agency conducted a study for Residence Inn by Marriott of business travelers who take trips of five nights or more. According to this study, 37% of these travelers enjoy sightseeing more than any other activity that they do not get to do as much at home. Suppose 120 randomly selected business travelers who take trips of five nights or more are contacted. What is the probability that fewer than 40 enjoy sightseeing more than any other activity that they do not get to do as much at home?

6.48 Suppose interarrival times at a hospital emergency room during a weekday are exponentially distributed, with an average interarrival time of nine minutes. If the arrivals are Poisson distributed, what would the average number of arrivals per hour be? What is the probability that less than five minutes will elapse between any two arrivals?

7.1 Develop a frame for the population of each of the following research projects.
a. Measuring the job satisfaction of all union employees in a company
b. Conducting a telephone survey in Utica, New York, to determine the level of interest in opening a new hunting and fishing specialty store in the mall
c. Interviewing passengers of a major airline about its food service

7.6 A city's telephone book lists 100,000 people. If the telephone book is the frame for a study, how large would the sample size be if systematic sampling were done on every 200th person?

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