5 Assorted Probability Questions

1. For a particular group of taxpayers, 25 percent of the returns are audited. Six taxpayers are randomly selected from the group.

a. What is the probability two are audited?
b. What is the probability two or more are audited?

2. On the average an artist sells two of her works per hour at weekend art shows. What is the probability of selling least one work this hour?

3. The mean life of certain type of refrigerator is approximately normally distributed with a mean of 7.2 years and a standard deviation of 1.9 years.

a. What fraction of the refrigerators last more than 10 years?
b. What fraction of the refrigerators last between 6 and 10 years?
c. What fraction of the refrigerators last more than 8 years but less than 10 years?
d. Suppose the manufacturer wants to establish a warranty so that only about 15 percent of the refrigerators will need to be repaired under the warranty. What is the cutoff point between those that will receive repairs under the warranty and those that will not?

4. A sample of 80 Chief Financial Officers revealed 20 had at one time been dismissed from a job. Develop a 94 percent confidence interval for the proportion that has been dismissed from a job.

5. A random sample of 20 retired Florida residents revealed they listened to the radio and average (mean) of 40 minutes per day with a standard deviation of 8.6 minutes. Develop a 95 percent confidence interval for the population mean listening time.