1. Suppose that 5 of a total of 20 company accounts are in error. An auditor selects a random sample of 5 out of the 20 accounts. Let X be the number of accounts in the sample that are in error. Is X binomial? If not, what distribution does it have? Explain.
2. According to a front-page article in The Wall Street Journal, 30% of all students in American universities miss classes due to drinking. If 10 students are randomly chosen, what is the probability that at most 3 of them miss classes due to drinking?
The Normal Distribution
3. The impact of a television commercial, measured in terms of excess sales volume over a given period, is believed to be approximately normally distributed with mean 50,000 and variance 9,000,000. Find 0.99 probability bounds on the volume of excess sales that would result from a given airing of the commercial.
4. The number of people responding to a mailed information brochure on cruises of the Royal Viking Line through an agency in San Francisco is approximately normally distributed. The agency found that 10% of the time, over 1,000 people respond immediately after a mailing, and 50% of the time, at least 650 people respond right after the mailing. Find the mean and the standard deviation of the number of people who respond following a mailing.
Sampling and Sampling Distributions
5. Explain why we need to draw random samples and how such samples are drawn. What are the properties of a (simple) random sample?
6. The Toyota Prius uses both gasoline and electric power. Toyota claims its mileage per gallon is 52. A random sample of 40 cars is taken and each sample car is tested for its fuel efficiency. Assuming that 52 miles per gallon is the population mean and 2.4 miles per gallon is the population standard deviation, calculate the probability that the sample mean will be between 52 and 53.
Confidence Intervals
7. The Java computer language, developed by Sun Microsystems, has the advantage that its programs can run on types of hardware ranging from mainframe computers all the way down to handheld computing devices or even smart phones. A test of 100 randomly selected programmers revealed that 71 preferred Java to their other most used computer languages. Construct a 95% confidence interval for the proportion of all programmers in the population from which the sample was selected who prefer Java.
8. A survey of 5,250 business travelers worldwide conducted by OAG Business Travel Lifestyle indicated that 91% of business travelers consider legroom the most important in-flight feature. (Angle of seat recline and food service were second and third, respectively.) Give a 95% confidence interval for the proportion of all business travelers who consider legroom the most important feature.