Homework#7 - 3 What is standard deviation of the number she...

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Stat 133 Autumn 2007 NAME Allison Heck Homework #7 (10 points) GROUP #_______________ Due Thursday Nov 15 (beginning of recitation) A quiz consists of 10 multiple choice questions. Each question has 4 possible answers, only one of which is correct. Pat plans to guess the answer for each question. Let X be the number of answers Pat gets right. 1. How many questions can we expect Pat to get right (over the long term)? mean = 10*.25 = 2.5 questions 2. What is the chance that Pat gets 5 or more questions right? n = 10 p = .25 Want: P(X>= 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = .0781 Suppose Pat’s midterm has 100 questions on it. The exam is also multiple choice, 4 possible answers each, one of which is correct. She again guesses at random for each question.
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Unformatted text preview: 3. What is standard deviation of the number she is expected to get right? n = 100 p = .25 standard deviation = (100*.25(1-.25))^(1/2) = 4.33 4. What is the chance that Pat gets more than 35 correct? Want: P(X>35) = 1- P(z<2.31) = 1 - .9896 = .0104 Mean = 100*.25 = 25 z = (35 – 25)/4.33 = 2.31 Suppose a gas station claims that 25% of all cars are low on oil. The station owner takes a random sample of 7 cars and checks their oil levels. She counts the number of cars in the sample that are low on oil. 5. What is the expected number of cars with low oil from this sample? mean = 7*.25 = 1.75 cars 6. What is the probability that at least 1 of the cars is low on oil? Want: P(X>=1) = 1 – P(X=0) = 1 – .1335 = .8665 1...
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