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On the Web, What kinds of Web sites do males aged $18$to $34$visit most often? Half of the male Internet users in this age group visit an auction site such as eBay at least once a month.$11$A study of Internet use interviews a random sample of $500$men aged $18$to $34$. Let $X$= the number in the sample who visit an auction site at least once a month.

(a) Show that $X$is approximately a binomial random variable.

(b) Check the conditions for using a Normal approximation in this setting.

(c) Use the Normal approximation to 铿乶d the probability that at least $235$of the men in the sample visit an online auction site at least once a month.

Several online textbook retailers advertise that they have lower prices than on-campus bookstores. However, an important factor is whether the Internet retailers actually have the textbooks that students need in stock. Students need to be able to get textbooks promptly at the beginning of the college term. If the book is not available, then a student would not be able to get the textbook at all, or might get a delayed delivery if the book is back ordered.

A college newspaper reporter is investigating textbook availability at online retailers. He decides to investigate one textbook for each of the following seven subjects: calculus, biology, chemistry, physics, statistics, geology, and general engineering. He consults textbook industry sales data and selects the most popular nationally used textbook in each of these subjects. He visits websites for a random sample of major online textbook sellers and looks up each of these seven textbooks to see if they are available in stock for quick delivery through these retailers. Based on his investigation, he writes an article in which he draws conclusions about the overall availability of all college textbooks through online textbook retailers.

Write an analysis of his study that addresses the following issues: Is his sample representative of the population of all college textbooks? Explain why or why not. Describe some possible sources of bias in this study, and how it might affect the results of the study. Give some suggestions about what could be done to improve the study.