课程名称： 统计学 课程性质： 整开 课程范围： Chapter 1 - Chapter 6 到 Poisson，不包含 Poisson process 开课教师： 丁兆平 开课学院： 商学院 开课系级： 统计系 考试日期(年月日)： 2013/11/12 考试时限(Mins)： 120 min 附注： 试题本文： 1. Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of times record for each method are shown. Times are in minutes. Automobile: 28 29 32 37 33 25 29 32 41 34 Public Transportation: 29 31 33 32 34 30 31 32 35 33 a. Compute the sample mean and standard deviation for each method. (10 pts) b. On the basis of your results from (a), which method of transportation should be preferred? Explain. (5 pts) c. Develop a box plot for each method and make sure to check for outliers. Does a comparison of the box plots support your conclusion in (b)? (15 pts) 2. A local bank reviewed its credit card policy with intention of recalling some its credit cards. In the past approximately 5% of the cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of 0.05 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is 0.2 for customers who do not default. Of course, the bank also found that the probability of missing a monthly payment for those who default is 1. a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default. (10 pts) b. The bank would like to recall its card if the probability that a custumer will default is greater than 0.2. Should the bank recall its card if the customer misses a monthly payment? Why or Why not? (5 pts) 3. The sales of Lexus automobiles in the Mucha area follow a Poisson distribution with a mean of 2 per day. a. What is the probability that no Lexus is sold on a particular day? (5 pts) b. What is the probability that for five consecutive days no Lexus is sold? (7 pts) c. What is the probability that for five consecutive days at least two Lexuses are sold? (8 pts) 4. Through the week ending September 16, 2001, Tiger Woods was the leading money winner on the PGA Tour. Of the top 10 money winners, seven players used a Titleist brand golf ball. Suppose that we randomly select two of the top 10 money winners. a. Determine the probability distribution for the number of selected money winners who used Titleist brand golf ball. (10 pts) b. Find the probability that exactly one uses a Titleist golf ball. (5 pts) 5. A psychologist determined the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let X be a random variable indicating the number of sessions required to gain the patient's trust. The following probability distribution has been proposed. p(x)=x/6 , x=1, 2, 3. a. Is this probability distribution valid? Explain. (5 pts) b. What is the probability that it takes at least 2 sessions to gain the patient's trust? (5 pts) c. Find the mean and standard deviation of the number of sessions required. (10 pts) --

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