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?
4. 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?
5. 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?
6. 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.
7. Daily water consumption in Mankato, MN, Averages 18.9 gallons per household, with
a standard deviation of 3.6 gallons. The city commissioner wishes to estimate this
unknown mean with a sample of 100 households. How likely is it the sampling error will
exceed .05 gallons?
8. An openion poll of 1000 residents of a large city asks whether they favor a rise in taxes
to pay for a new sports stadium. If more than 85% support the tax, a referendum will be
introduced in the city’s next election. If the unknown population proportion of all
residents who favor the tax is 82%, what is the probability it will be placed on the next
ballot?
9. The diameter of Ping-Pong balls manufactured at a large factory is expected to be
normally distributed with a mean of 1.30 inches and a standard deviation of .04 inch.
What is the probability that a randomly selected Ping-Pong ball will have a diameter
a) Between 1.28 and 1.30 inches?
b) Between 1.31 and 1.33 inches?
C) Between what two Values (symmetrically distributed around the mean) will
60% of the Ping-Pong balls fall(in terms of diameter)?
D) If many random sample of 16 balls are selected
1) What is the mean and standard error of the mean be expected to be?
2) What distribution would the sample mean follow?
3) What proportion of the sample means would be between 1.28 and 1.30
inches?
4) What proportion of the sample means would be between 1.31 and 1.33
inches?
e) Compare the answers of (a) with (d)(3) and b with (d)(4). Discuss.
f) Explain the difference in the results of © and (d)(5).
g) Which is more likely to occur-an individual ball 1.34 inches, a sample mean
above 1.32 inches in a sample size of 4, or a sample mean above 1.31 inches in a
sample size of 16? Explain.
10. Carol spent all weekend partying and knows absolutely nothing about the 10
true/false questions on a Monday morning economics quiz. What is the probability that
she gets at least 8 right by simply guessing?
11. 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.
12. 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.
13. 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.
14. 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?
15. 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?
16. 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%?
17. 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?
18. 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!!!