Name _____________________________ Section _______ PID ________________ STT 315 HW # 2 (10 points) 2/11/10 Gilliland (Due at recitation on Feb 18 ? not accepted late) SHOW YOUR WORK Concepts used: binomial distribution, hypergeometric distribution, exponential distribution 1. Suppose that a certain coin lands H with probability .6 and T with probability .4 when it is tossed. It is to be given n = 100 independent tosses. Let X denote the number of times the coin lands H across the 100 tosses. Here is a plot of the binomial probability distribution. (a) P(X = 50) = __________ How did you perform the calculation? ____________________________ (b) P(X < 50) = __________ How did you perform the calculation? ____________________________ (c) E(X) = __________ SD(X) = __________ (d) Taking the distribution of X to be , calculate P(X < 50) = __________ What calculator or computer and software did you use to perform the calculation? __________________________________________ 2. You direct a company that has 48 middle mangers of whom 16 are women. All 48 employees have similar experience, education and evaluations. Nine will be selected for promotion. How many of the promotions do you ?expect? to go to women? _______ Would you think it unusual if no women are selected? _______ (There are no right or wrong answers here.) (a) If the promotion process is to select a random sample of 9 employees from the 48 employees to receive a promotion, what is the chance that no women are promoted? ______________ (b) If the promotion process is to select a random sample of 9 employees from the 48 employees to receive a promotion, what is the chance that one or fewer women are promoted? _______________ 3. A manufacturer of 100W light bulbs has data that suggest that the lifetimes X of its light bulbs follow an exponential distribution with mean 2000 hours. Use this exponential model to answer the following questions about a randomly selected light bulb from the manufacturer. .0005 (a) Write the density function of X. f(x) = _____________, x > 0. Sketch f. 2000 4000 x (b) What is the probability that it will fail in the first 1500 hours, i. e., what is P(X ? 1500)? ________________
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