Review for Exam I
Econ 207
Dr. Khan
1.a.
For the following sample, compute and interpret its mean, median, mode,
variance, and standard deviation. (Sample is amount of money spent on textbooks by
random students at MSU, Fall 2001)
105
115
135
95
94
85
98
90
78
75
77
85
84
95
74
87
89
97
99
92
109
105
102
111
112
122
102
123
124
93
132
133
82
95
91
85
b. Compute and interpret second quartile.
c. What is the z-score if spending on textbooks is $95. Interpret the z-score.
d. Construct frequency, percentage frequency, and cumulative relative frequency
distributions with six classes for the above sample data.
e. Construct a histogram and a pie chart for the data. (hint: use part (d))
f. Compute and interpret the mean and standard deviation of the group data in part (d)
g. Is the variable “money spend on textbooks” discrete? Why or why not?
2. Problem 31(page 93).
3. The results of an automobile ownership survey are summarized in the following table.
Location
--------------------------------------------------Type of Car Owned
Large City
Suburb
Rural
------------------------------------------------Foreign
90
60
25
Domestic
110
90
125
a. What is the probability that a rural resident owns domestic car?
b. What is the probability that a person owns a foreign car?
c. Given that an individual lives in a suburb, what is the probability that he/she owns a
domestic car?
d. Are the events “ Owns a foreign Car” and “Rural” independent?
4. A Jar holds five red, six white, and 7 blue jellybeans. If you pick three jellybeans at
random without replacement, what is the probability of getting at least two blue ones?
5. Solve problem no 4. with the assumption of with replacement.
6. The economics department at MSU has access to three fax machines. The probability
each is out of service is 20/100, 25/100, 30/100 respectively. Assuming independence,
find the probability that
a. none of them is out of service.
b. one machine is out of service.
c. at most two machines are out of service.
d. at least two machines are out of service.
7. Marry is taking two courses, photography and economics. Student records indicate
that probability of passing photography is .75, that of failing economics is .65, and that of
passing at least one courses is .85. Find the probability of the following.
a. Marry will pass economics.
b. Marry will pass both courses.
c. Marry will fail both courses.
d. Marry will pass exactly one course.
8. If a die is rolled once, E is the event “getting a 4,” and F is the event “getting a odd
number.” Use probabilities to determine whether (a) E and F are independent and (b) E
and F are mutually exclusive.
9. A pair of dice is rolled. Find the probabilities of the given events.
a. the sum is 6.
b. the sum is 6 or 9.
c. the sum is even and less than 5.
d. the sum is even or less than 5.
d. the sum is 7 or the 1st die is less than 5.
e. the sum is 6, given that sum is even.
10. A card is drawn at random from a poker hand. What is the probability that the card is
a club given that the card is a king?
**Note: Review the lecture notes, homework problems, and quizzes.