# hw4 - STAT 225 Homework 4 Due Tuesday June 2 Comments 1...

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STAT 225 - Homework 4 Due Tuesday June 2 Comments: 1. This homework is due Tuesday, June 2 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must always SHOW ALL WORK. If you do not show your work, you may not receive full credit. Do the following problems. 1. Page 113, problem 3.56 2. A small commuter plane has 30 seats. The probability that any particular passenger will not show up for the flight is .10, independent of the other passengers. The airline sells 32 tickets for the flight. What is the probability that more passengers show up than there are seats available? 3. Let Y Bin (5 , 1 3 ). Find E (4 Y ) Guidance: Use the Binomial expansion: n X k =0 n k ! · a k · b n - k = ( a + b ) n 4. Page 119, problem 3.71 Note: The text uses the notation q for 1 - p . Guidance: Look at how we found the probabilities in parts (a) and (b) in the 5/28 lecture (lecture 8, pages 3 and 4 of the handout), and follow the same reasoning. Again, remember that q = 1 - p 5. A poll that was conducted in August 2007 estimated that 62% of registered voters in the US agree with the 1973 Roe v. Wade Supreme Court decision that establishes a woman’s right to an abortion (i.e., 62% are “pro-choice”) Suppose that soon after the results of this poll were released another poll on the same issue was conducted in which registered voters were chosen at random and contacted. (a) What is the probability that the fifth person that is contacted is the first to be pro- choice. (Does it make intuitive sense to you why this probability is so small?) (b) what is the probability that more than 2 people will have to be contacted in order to find the first person who is pro-choice? (c) Given that none of the first 5 people who were contacted was pro-choice, what is the probability that at least three more people will need to be contacted in order to find one? 1

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6. A telemarketer selling subscriptions to a local newspaper has a sales quota of six subscriptions per night. Normally, only one in four people contacted by telephone agrees to purchase a subscription to the newspaper. However, due to exceptional sales skills, this telemarketer’s
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