Table 1P(X

1. (10 points) A survey of MBA students reveals that among GMAT scorers above 750, 52% took a preparatory course, whereas among GMAT scorers of less than 750 only 23% took a preparatory course. An applicant to an MBA program has determined that he needs a score of more than 750 to get into a top 20 MBA program, but he feels that his probability of getting that high a score is quite low - 20%. He is considering taking a preparatory course that costs only $50. He is willing to do so only if his probability of achieving 750 or more doubles. Draw the probability tree. What should he do - spend $50 or not? 2. (10 points) In the advertisements for a large university, the dean of the School of Business claims that the average salary of the school's graduates one year after graduation is $800 per week, with a standard deviation of $100. A second-year student in the business school who has just completed his statistics course would like to check whether the claim about the mean is correct. He does a survey of 25 people who graduated one year earlier and determines their weekly salary. He discovers the sample mean to be $750. Test the null hypothesis that the dean's claim is correct (u = 800) against the alternative hypothesis that u is smaller than 800 (u