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!!!