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Statistics questions

1. The table below describes the smoking habits of a group of asthma sufferers.

Nonsmoker Occasional Regular Heavy Total
_________ Smoker Smoker Smoker_______
Men 424 39 72 36 571
Women 360 46 77 44 527_
Total 784 85 149 80 1098

a. If one of the people is randomly selected, find the probability of getting someone who is a regular or heavy smoker. (5 points)

b. If one of the people is randomly selected, find the probability the person is a nonsmoker given the person is a woman. (5 points)

c. Assuming we were to consider a random sample of 15,000 people, how many would you predict are women and heavy smokers based on the results given here? (5 points)

2. A company with equipment on multiple lines used to manufacture its products schedules each line for maintenance on a weekly basis. This scheduled maintenance is a complete check of the line that includes any needed adjustments to the equipment. When this scheduled is followed there is a 0.02 probability that line's equipment will need additional minor maintenance the day of the scheduled service, a 0.10 probability it will need minor maintenance the first day following the service, a 0.27 probability it will need minor maintenance the second day following service, a 0.43 it will need minor maintenance the third day and a 0.18 probability it will need minor maintenance the fourth day following the scheduled service. (This covers the 5 regular working days for the plant. Hint: Let 0 represent the day of the scheduled service.)

a. Set up a probability distribution to describe this situation. (2 points)
b. Based on this schedule for full maintenance of the lines, how often should they expect to need to complete minor maintenance? (This would be the mean of the distribution.) Be sure to explain what this number represents.

c. How much would this value reasonably be expected to fluctuate? (This is the standard deviation.) Be sure to explain what this number represents.

d. What's the probability of needing to do maintenance within the first three days following the scheduled service?

3. Based on past records 7% of the loans authorized by the branch manager of a local bank each month will never be repaid.

a. What is the probability that 5 from a sample of 22 loans this past moth will not be repaid?

b. What is the probability that at most 3 from a sample of 22 loans this past month will not be repaid?

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