課程名稱︰統計學一上 課程性質︰必修 課程教師︰雷立芬 開課學院：管理學院 開課系所︰國企系 考試日期（年月日）︰97.12.03 考試時限（分鐘）：三小時 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.The Laurier Company's brand has market share of 20%. Suppose that in a survey 1000 consumers of the product are asked which brand they prefer. What is the probability that more than 22% of the respondents say they prefer the Laurier brand? (5%) 2.The manager of a restaurant believes that waiters and waitresses who introduced themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the fomer group is 18% whereas that of the latter is only 15%. If tips are normally distributed with a standard deviation of 3%, what is the probability that in a random sample of 10 tips recorded from waiters and waitresses who introduce themselves and 10 tips from waiters and waitresses who don't, the mean of the former will exceed that of the latter? (7%) 3.Suppose interarrival times at a hospital emergency room during a weekday are exponentially distributed, with an average interarrival time of 9 minutes. If the arrivals are Poisson distribution, what would the average number of arrivals per hour be? What is the probability that less than 5 minutes will elapse between any two arrivals? (10%) 4.Suppose that X is a binomial random variable with n=30 and p=0.5. Find the following probabilities using normal approximations: p(X=2), p(X≧5). (10%) 5.The final marks in a statistics course are normally distributed with a mean of 70 and a standard deviation of 10. The professor must convert all marks to letter grades. She decides that she wants 10% A's, 30% B's, 40% C's, 15% D's, 5% F's. Determine the cutoff each letter grade. (10%) 6.The following function is the density function for the random variable X: x-1 f(x)= ── , 1 < x < 5 8 a.Graph the density function. (5%) b.Find the probability that X lies between 2 and 4. (3%) c.What is the probability that X is less than 3? (2%) 7.The bivariate distribution of X and Y is shown as follows │ X │ 1 2 ──┼─────── 1│0.28 0.42 Y │ │ 2│0.12 0.18 a.Find the marginal probability distribution of X. (3%) b.Find the marginal probability distribution of Y. (3%) c.Compute the mean and variance of X. (5%) d.Compute the mean and variance of Y. (5%) e.Compute the coefficient of correlation between X and Y. (7%) f.Determine the mean and varience or 2X-3Y. (5%) 8.A survey of middle-age men reveals that 33% of them are balding at the crown of their heads. Moreover, it is known that such men have an 18% probability of suffering a heart attack in the next 10 years. Men who are not balding in the way have 11% probability of a heart attack. Find the probability that a middle-age man will suffer a heart attack sometime in the next 10 years. (10%) 9.Your favorite team is in the final playoffs. You have assigned a probability of 60% that they will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over; your team has lost. What is the probability that they will win the series? (10%) --

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