A search engine company claims that 20% of people who use its site click for more information about its advertisers’ products. Assuming that claim is true,

  1. A search engine company claims that 20% of people who use its site click for more information about its advertisers’ products. Assuming that claim is true,

(a)  what is the probability that at least one out of the next 8 people who use the site will click for more information?

(b)  Estimate, using the normal distribution, the probability that at least 10 out of the next 80 people who use the site will click for more information.

(c)  Write a few sentences describing why the answer to (b) is higher than the answer to part (a).  Why would the answer be even higher if you estimated the probability that at least 1000 out of 8000 click for more info?

  1. An accountant is studying the time it takes a company to make payments on accounts payable. The mean time it takes to pay off an invoice is 13.6 days with a standard deviation of 4.3 days, and the times are normally distributed.

(a)  What is the probability that an account is paid off in less than 16 days?

(b)  Find the 95th  percentile for the payoff time- that is, a time for which 95% of the

accounts are paid off in less than that time.

(c)  The company has just received 29 invoices.  Find the probability that the mean payoff

time for these invoices is more than 16 days.

  1. Suppose heights of U.S. adults are normally distributed with a mean of 66.3 and a standard deviation of 4.4 inches.
  • Find the height such that 95% of the population is less than this height. (the 9 percentile)
  • What percent of US adults are taller than 64 inches?
  • What is the probability that a sample of 18 adults will have a mean height greater than 64 inches?
  1. In a poll, 527 out of 775 New York voters surveyed indicated that they approve of the job DeBlasio has done as mayor. Make a 99% confidence interval for the percentage of all New York voters who would approve of DeBlasio’s performance as mayor.  Describe the meaning of the interval that you found.
  1. Refer to the study quoted below (from USA Today newspaper)

What is the population, parameter, sample, and statistic in this study?  What type of data was collected?

“In one study, in the American Journal of Obstetrics & Gynecology, Kaiser Permanente researchers analyzed information about caffeine drinking by 1,063 women early in their pregnancies.

Women who reported drinking less than 200 milligrams of caffeine per day (about two cups of regular coffee or five cans of caffeinated soda) were 40% more likely to miscarry than women who said they drank no caffeinated beverages. Those who drank 200 milligrams or more of caffeine per day had about twice the miscarriage risk as women who drank none.”

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