• Document: AP Statistics Quiz A Chapter 17
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AP Statistics Quiz A – Chapter 17 Name The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. 1. How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood? 2. What is the probability that the tenth blood donor is the first donor with Type B blood? 3. What is the probability that exactly 2 of the first 20 blood donors have Type B blood? 4. What is the probability that at least 2 of the first 10 blood donors has Type B blood? 5. The blood drive has a total of 150 donors. Assuming this is a typical number of donors for a school blood drive, what would be the mean and standard deviation of the number of donors who have Type B blood? 6. Surprised by the low number of Type B blood donors at the blood drive, the American Red Cross wonders if the 11% estimate was too high for your area. How many Type B blood donors would it take to convince you that this estimate might be too high? Justify your answer. 17-5 AP Statistics Quiz A – Chapter 17 – Key The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. 1. How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood? This is a Geometric model with p = 0.11. 1 1 Expected value: µ = = = 9.1 donors p 0.11 2. What is the probability that the tenth blood donor is the first donor with Type B blood? 9 ( ) ( P 9 not Type B, Type B on 10 th = 0.89 ) (0.11) = 0.0385 3. What is the probability that exactly 2 of the first 20 blood donors have Type B blood?  20 2 18 P exactly 2 out of 20 = P X = 2 =   0.11 0.89 ( ) ( ) ( )( ) = 0.2822  2 4. What is the probability that at least 2 of the first 10 blood donors has Type B blood?  10 0 10  10 1 9 P X ≥ 2 = 1 − P X ≤ 1 == 1 −   0.11 0.89 ( ) ( ) ( )( ) +   0.11 0.89  = 1 − 0.6972 = 0.33028 ( )( )  0   1  5. The blood drive has a total of 150 donors. Assuming this is a typical number of donors for a school blood drive, what would be the mean and standard deviation of the number of donors who have Type B blood? Using the Binomial model, Mean: µ = np = 150 0.11 = 16.5 ( )( ) Standard deviation: σ = npq = (150)(0.11)(0.89) = 3.83 6. Surprised by the low number of Type B blood donors at the blood drive, the American Red Cross wonders if the 11% estimate was too high for your area. How many Type B blood donors would it take to convince you that this estimate might be too high? Justify your answer. Since np = 16.5 and nq = 133.5 , we expect at least 10 successes and 10 failures. The sample size is large enough to apply a Normal model. It would be unusual to see the number of Type B donors more than 2 standard deviations below the mean. Since the standard deviation is 3.83, it would be unusual to see fewer than 9 Type B blood donors since 16.5 – 2(3.83) = 8.84. So, I would conclude that the 11% estimate is too high for my area if there were fewer than 9 Type B blood donors. NOTE: Other students might apply different criteria. 17-6 AP Statistics Quiz B – Chapter 17 Name The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of customers for a day, and whether they purchase specialty clothes for their pet. 1. Assuming the pet store owner is correct in thinking that only 4% of her customers purchase specialty clothes for their pets, how many customers should she expect before someone buys a garment for their pet? 2. What is the probability that she does not sell a garment until the 7th customer? Show work. 3. What is the probability that exactly 3 of the first 10 customers buy specialty clothes for their pet? Show w

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