TA Review 1 2003.11.5
1. In an application for a credit card, potential customers are asked for their social security
numbers. A social security number is an example of a
a. qualitative variable
b. quantitative variable
c. qualitative or quantitative variable, depending on how the respondents answered the question
d. ratio variable
e. None of these answers is correct.
ANSWER: a
2. You are given the following data on the ages of employees at a company. Construct a stem-and-leaf display. Specify the leaf unit for the display.
26 32 28 45 58
52 44 36 42 27
41 53 55 48 32
42 44 40 36 37
ANSWER: Leaf Unit = 1
2 | 6 7 8
3 | 2 2 6 6 7
4 | 0 1 2 4 4 5 8
5 | 2 3 5 8
3. The grades of 10 students on their first management test are shown below.
94 61 96 66 92
68 75 85 84 78
a. Construct a frequency distribution. Let the first class be 60 - 69.
b. Construct a cumulative frequency distribution.
c. Construct a relative frequency distribution.
ANSWERS:
a. b. c.
Cumulative Relative
Class Frequency Frequency Frequency
60 - 69 3 3 0.3
70 - 79 2 5 0.2
80 - 89 2 7 0.2
90 - 99 3 10 0.3
Total 10 1.0
3. A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. Their responses are given below.
2 1 0 2 0 2 1 2 0 2 1 2
Using this data set, compute the
a. mode
b. median
c. mean
d. range
e. interquartile range
f. variance
g. standard deviation
h. coefficient of variation
ANSWERS:
a. 2
b. 1.5
c. 1.25
d. 2
e. 1.5 by IRQ=Q3-Q1
f. 0.75
g. 0.866
h. 69.28% by
4. You are given the following information on Events A, B, C, and D.
P(A) = .4 P(A È D) = .6
P(B) = .2 P(AôB) = .3
P(C) = .1 P(A Ç C) = .04
P(A Ç D) = .03
a. Compute P(D).
b. Compute P(A Ç B).
c. Compute P(AôC).
d. Compute the probability of the complement of C.
e. Are A and B mutually exclusive? Explain your answer.
f. Are A and B independent? Explain your answer.
g. Are A and C mutually exclusive? Explain your answer.
h. Are A and C independent? Explain your answer.
4.
ANSWERS:
a. 0.23 by P(A È D) = P(A)+ P(D)- P(A Ç D)
b. 0.06 by P(A Ç B) =P(AôB) P(B)
c. 0.4 by P(AôC) = P(A Ç C)/ P(C)
d. 0.9 by P(C) =1-P(C)
e. No, P(AôB) ¹ 0
f. No, P(AôB) ¹ P(A)
g. No, P(A Ç C) ¹ 0
h. Yes, P(AôC) = P(A)
5. In a city, 60% of the residents live in houses and 40% of the residents live in apartments. Of the people who live in houses, 20% own their own business. Of the people who live in apartments, 10% own their own business. If a person owns his or her own business, find the probability that he or she lives in a house.
ANSWER: 0.75
( a person lives in a house| a person owns business )=
1