Review for Exam II Econ 207 Dr. Khan Note: Review the lecture notes, homework problems, and quizzes. 1. A set of final examination grades in an introductory statistics course was found to be normally distributed with a mean of 73 and a variance of 64. a. What is the probability of getting a score of 91 on this exam? b. What percentage of students scored between 65 and 89? c. What is the final exam grade if only 5% of the students taking the test scored lower? 2. The dean of a business school wishes to form an executive committee of 5 from among the 40 tenured faculty members at the school. The selection is to be random, and at the school there are 8 tenured faculty members in accounting. What is the probability that the committee will contain? a. None of the accounting faculty? b. at least one of them? 3. A family has five smoke alarms in their home, all battery operated and working independently of each other. Each has reliability of 90% - that is, has a 90% chance of working. If fire breaks out, what is the probability that at least two of them will sound the alarm? 5. The chance that any given taxicab in New York will be involved in an accident in any one month is .02. If a particular cab company has 300 cabs on the street, what is the probability that at least 12 will be in an accident this month? 6. Airplanes arrive at Chicago O’Hare airport at the average rate of 5.2 per minute. Air traffic controllers can safely handle a maximum of four airplanes per minute. What is the probability that airport safety is jeopardized? 7. Given the following probability distribution: X P(X) 0 .5 1 .2 2 --3 .10 4 .05 Find the following: a. Expected value b. Variance c. Standard deviation. 8. A sample of 12 donations by political action committees to congressional campaign funds was recorded, in thousands of dollars, as 12.1, 8.3, 15.7, 9.35, 14.3, 12.9, 13.2, 9.73, 16.9, 15.5, 14.3, and 12.8. Calculate and interpret a 98% confidence interval for the mean donation by PACs. 9. In a 1996 survey of 1000 American citizens, 300 respondents claimed to be fluent in a second language. Find a 94% confidence interval for the true proportion of citizens who are not fluent in a second language. 10. A company wants to estimate the length of Friday lunch breaks taken by salaried executives. One Friday, 30 executives were monitored and the average of lunch break was 94.5 minutes with a standard deviation of 25 minutes. Calculate 90%, 95%, and a 99% confidence intervals. 11. A marketing manager of a long distance telephone company plans to estimate the average amount of money spent monthly by male college students. It is reasonable to assume that = 1.8 dollars. How large a sample is needed so that it will be possible to assert with 95% confidence that sample mean is off by less than a quarter? 12. The dean of a private university wants an estimate of the number of out-of state students enrolled. She must be 97% confident that the error is less than 4 percent. How large a sample must she take? If the sample reveals a proportion of 31 percent out ofstaters, and there are 12, 414 students, how many do you estimate come from other states? 13. The manager of a mutual fund claims that his fund has averaged a return of 10.2 percent per year with a standard deviation of 3.5 percent for his clients over the past several years. If a sample of 10 investors reported a mean rate of 9.6 percent, are you inclined to believe the fund manager? Do your conclusion change, if you have a sample of 100? Why or why not? 14. The director of admissions at a large university would like to advise parents of incoming students concerning the cost of textbooks during a typical semester. A sample of 22 students enrolled in the university indicates a sample average cost of 315.40 with a standard deviation of 43.20. Should the director tell parents that the average cost on textbooks is more than $300? 15. The personal director of a large insurance company is interested in reducing the turnover rate of data processing clerks in the first year of employment. Past records indicates that 25% of all new hires in this area no longer employed at the end of 1 year. Extensive new training approaches are implemented for a sample of 150 data processing clerks. At the end of a 1 year period, of these 150 individuals, 48 are no longer employed. Is there evidence that the true turnover rate is less than .25? Use = .03 16. The popularity of Video games sparked interest among arcade owners regarding the relative merits of different types of amusement. A sample of 40 “flipper and bumper” games yielded a mean weakly revenue of $280 with a standard deviation of $81. A like number of electronic games produced a mean revenues of $297 with S = $72. At the 1% level of significance, is there a difference between two games in their ability to generate revenue? 17. A man wants to compare Lotus 1-2-3, which is used in his firm, with Microsoft Excel, which is not used in his firm. He used Microsoft Excel 12 times to calculate a certain procedure. On average it took 7.2 minutes with a standard deviation of .87 minutes. When he used Lotus 1-2-3 10 times, it took 7.9 minutes with a standard deviation of .97 minutes to do the same task. Should he suggest to his boss that the firm use Microsoft Excel? 18. Steve, a security analyst, have always felt that convertible bonds are more likely to be overvalued than are income bonds. Of 312 convertible bonds examined last year, Steve found 202 to be over valued, while 102 of the 205 income bonds proved to be overvalued. Do these data support Steve’s assumption? Use = .01. 19. The manager of a local grocery store, Grocery Mart, has found out that 30 percent of local people prefer their store. If a random sample of 220 local people were selected, what is the probability that the sample proportion of people who prefer Grocery Mart will range from 20% to 30%? 20. The sign in an elevator states, “ Maximum Capacity 2500 pounds or 16 people.” If the weights of people are normally distributed with a mean of 150 pounds and standard deviation of 20 pounds, what is the probability that 16 people weigh more than 2500 pounds? 21. What is Central Limit Theorem? Why it is important? Explain in details. ** Review all the homework problems, problems in the lecture note and quizzes. Then solve this worksheet. Good Luck!!!