1. A search engine site claims that, on average, one out of five visitors clicks on an ad.
(a) If 8 users visit the site, what is the probability that at least three click on an ad? b) If 8 users visit the site, what is the probability that less than two of them click on an ad? c) If 800 users visit the site, would the probability that less than 200 click on an ad be higher or lower than the answer found in part (b)? Write a few sentences explaining your answer- computations are not required (or desired) d) Suppose 90 users visit the site during a particular minute, use the normal approximation to estimate the probability that more than 25 of them click on an ad. e) If 900 users visited the site, would the probability that more than 250 of them click on an ad be higher or lower than the answer found in part (d)? Write a few sentences explaining your answer- computations are not required (or desired)
2. Suppose that, overall, 5% of all tax returns are audited by the IRS. (a) If an accountant has 7 clients for whom she prepared tax returns, what is the probability that less than 3 will be audited? (b) If the accountant has 30 clients, what is the probability that at least one is audited? (c) Suppose the accountant prepares 500 returns, use the normal approximation to estimate the probability that more than 20 of the returns are audited.
3. Suppose the weight of eggs produced by Henly Farms has a mean of 59.7 g. with a standard deviation of 3.4 g. Find the probability that a carton of a dozen eggs will weigh less than 727 g.
4. Magazine Marketers is holding a sweepstakes. They list the following prizes and the probability of winning the prize:
To enter the sweepstakes, you must pay $1 for postage. Find the expected profit for someone entering this sweepstakes.
6. Given below are the birth weights of babies born to mothers who took special vitamin supplements while pregnant: 3.13 4.37 3.93 4.33 3.39 3.68 4.68 3.52 3.02 4.29 2.47 4.13 4.47 3.22 3.43 2.54 a. Make a 99% confidence interval for the mean weight of babies whose mothers take vitamin supplements. b. Do a hypothesis test to determine if these babies weight is more than the mean weight for the population of all babies which is 3.39 kg using α = .005 c. In a short paragraph, describe the relationship between your answer to part (a) and your answer to part (b).
8. In a study of the effectiveness of a new pain killer, 46 out of 821 patients tested reported experiencing side effects. Use α = 0.01 significance level to determine if the proportion who experience side effects from this drug is lower than the 7.8% rate of side effects for the older version of this medication.