Statistics In Mathematics

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Math 234 - HW#2 Name _____________________ 10:30 12:30 12:00T-TH You must show your answers clearly and use proper notation. I will not accept work or answers squeezed in the margin 1. Many companies test prospective employees for drug use. Suppose a company uses a test that is 98% accurate – that is it correctly identifies an applicant as a user or nonuser with probability .98. The test is performed on each applicant twice and the outcomes are independent. a) Use a tree diagram to sketch this two stage experiment. b) Find the probability that a nonuser fails both tests. c) Find the probability that a user fails at least one test. d) Find the probability that a user passes both tests. 2. Two representatives are randomly selected from a list of six people, 4 male, 2 females.Let the random variable X represent the number of females selected. a)Construct a probability distribution table for the random variable X. b)What is the probability that there will be at least one female representative? c) What is the probability that there will at most one female representative? d) Calculate the mean and standard deviation for the random variable X. 3. Suppose a basketball player, Player A, made 80% of her free throw attempts last season and that she continues to shoot free throws at the same rate. Assume that free throw attempts are independent. Let the random variable X be the number of free throws that player A makes in her next 15 attempts. a) What is the distribution of X? b) Find the mean and standard deviation of X. c) Find the probability that player A makes exactly 10 free throws. d) Find the probability that player A makes at least 8 free throws. 4. Suppose it is observed that, on average, 35 people are admitted to the intensive care unit of a particular hospital every week. Let the random variable

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