TA Review
2004.11.18
1. The frequency distribution below was constructed from data
collected on the quarts of soft drinks consumed per week
by 20 students.
Quarts of Soft Drink
Frequency
0 3
4
4 7
5
8 - 11
6
12 - 15
3
16 - 19
2
a. Construct a relative frequency distribution.
b. Construct a cumulative frequency distribution.
c. Construct a cumulative relative frequency
distribution.
ANSWERS:
Quarts of
Soft Drinks
0 - 3
4 - 7
8 - 11
12 - 15
16 - 19
Total
Relative
Frequency
0.20
0.25
0.30
0.15
0.10
1.00
Cumulative
Frequency
4
9
15
18
20
Cumul. Relative
Frequency
0.20
0.45
0.75
0.90
1.00
2. The SAT math scores of a sample of business school students
and their genders are shown below.
SAT Math Scores
Gender < 400
400~ 600
> 600
Total
Female 24
168
48
240
Male
40
96
24
160
Total
64
264
72
400
a. How many students scored less than 400?
b. How many students were female?
c. Of the male students, how many scored 600 or more?
d. Compute row percentages and comment on any relationship
that may exist between SAT math scores and gender of the
individuals
e. Compute column percentages.
ANSWERS:
a.
64
b.
240
c.
24
d.
SAT Math Scores
Gender
< 400
400~600 >600
Total
Female
10%
70%
20%
100%
Male
25%
60%
15%
100%
1
From the above percentages it can be noted that the
largest percentages of both genders' SAT scores are in
the 400 to 600 range. However, 70% of females and only
60% of males have SAT scores in this range. Also it can
be noted that 10% of females' SAT scores are under 400,
whereas, 25% of males' SAT scores fall in this category.
e.
Gender
Female
Male
Total
< 400
37.5%
62.5%
100%
SAT Math Scores
400~600
>600
63.6%
66.7%
36.4%
33.3%
100%
100%
3. The following data represent the daily demand (y in
thousands of units) and the unit price (x in dollars) for
a product.
Daily Demand (y)
Unit Price (x)
47
1
39
3
35
5
44
3
34
6
20
8
15
16
30
6
a. Compute and interpret the sample covariance for the
above data.
b. Compute and interpret the sample correlation
coefficient.
ANSWERS:
a.
-160.14 (rounded). Since the covariance is
negative, it indicates a negative relationship
between x and y.
b.
-0.922. There is a strong negative relationship
between daily demand and unit price.
4. The following is a frequency distribution for the ages of
a sample of employees at a local company.
Age
Frequency
30 - 39
2
40 - 49
3
50 - 59
7
60 - 69
5
70 - 79
1
a. Determine the average age for the sample.
b. Compute the variance.
c. Compute the standard deviation.
d. Compute the coefficient of variation.
ANSWERS:
a.
54.5
2
b.
117.65
c.
d.
10.85
19.91%
5. All the employees of ABC Company are assigned ID numbers.
The ID number consists of the first letter of an employee’s
last name, followed by four numbers.
a.
How many possible different ID numbers are there?
b.
How many possible different ID numbers are there
for employees whose last name starts with an “A”?
ANSWERS:
a. 260,000
b. 10,000
6. Six vitamin and three sugar tablets identical in appearance
are in a box. One tablet is taken at random and given to
Person A. A tablet is then selected and given to Person
B. What is the probability that
a. Person A was given a vitamin tablet?
b. Person B was given a sugar tablet given that Person A
was given a vitamin tablet?
c. neither was given vitamin tablets?
d. both were given vitamin tablets?
e. exactly one person was given a vitamin tablet?
f. Person A was given a sugar tablet and Person B was given
a vitamin tablet?
g. Person A was given a vitamin tablet and Person B was
given a sugar tablet?
ANSWERS:
a. 6/9
b. 3/8
c. 1/12
d. 5/12
e. 1/2
f. 1/4
g. 1/4
7. 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
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