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Finding probability of prescription orders

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Pharmacies continually monitor their prescription filling process. A local pharmacy has noted that the time to fill a prescription for a generic antibiotic is normally distributed, with a mean of 13.3 minutes and a standard deviation of 2.8 minutes.

a. Find the probability that a prescription for a generic antibiotic takes at least 10 minutes to fill.
b. Find the probability that the prescription for a generic antibiotic takes between 12 and 15 minutes to fill.
c. The slowest 20% of prescriptions fills result in a special discount to the customer. How long must a prescription fill for a generic antibiotic take in order to qualify for this discount?

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Normal probability

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1.(use the Normal Probability file)
In a recent year, about two-thirds of U.S. households purchased ground coffee. Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a normal random variable with a mean of $45.16 and a standard deviation of $10.00.
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d)99% of the households spent less than what amount?

2.(use the Normal Probability file)
The mean download time for the H&R Block Web site, www.hrblock.com, is 2.5 seconds. Suppose that the download time is normally distributed with a standard deviation of 0.5 second. What is the probability that a download time is
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b)between 0.5 and 1.5 seconds?
c)above 0.5 second?
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3.(use the confidence interval file)
The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.995 gallon.
a)construct a 99% confidence interval estimate of the population mean amount of paint included in a 1-gallon can
b)on the basis of these results, do you think the manager has a right to complain to the manufacturer? Why?

4.(use the confidence interval file)
In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below and stored in the file insurance.xls:
73 19 16 64 28 28 31 90 60 56 31 56 22 18
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a) construct a 95% confidence interval estimate of the mean processing time.
b) what assumption must you make about the population distribution in (a)?

5.(use the confidence interval file)
A large number of companies are trying to reduce the cost of prescription drug benefits by requiring employees to purchase drugs through a mandatory mail-order program. In a survey of 600 employees, 126 indicated that they either had a mandatory mail-order program in place or were adopting one by the end of 2004.
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b)Using the gender data only, conduct a 95% confidence interval of the proportion of female employees at Cumba, Inc.
c)In one or two sentences, interpret the results.

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