Barstow Community College Construct a Frequency Table for The Data Questions

BCC Math 2 Final Exam Form 625
Spring 2021
Professor Yuan
Name ___________________________________
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Solve the problem.
1) The data below show the types of medals won by athletes representing the United States in
the Winter Olympics.
gold
bronze
gold
gold
gold
gold
silver
gold
silver
silver
silver
bronze
gold
silver
bronze
bronze
bronze
bronze
bronze
silver
silver
gold
1)
silver
gold
silver
a. Construct a frequency table for the data.
b. Construct a relative frequency table for the data.
c. Construct a frequency bar graph for the data.
2) The amount of television viewed by today’s youth is of primary concern to Parents Against
Watching Television (PAWT). 300 parents of elementary school-aged children were asked
to estimate the number of hours per week that their child watches television. The mean
and the standard deviation for their responses were 19 and 2, respectively. PAWT
constructed a stem-and-leaf display for the data that showed that the distribution of times
was a symmetric, mound-shaped distribution. Give an interval where you believe
approximately 95% of the television viewing times fell in the distribution.
1
2)
3) A local newspaper claims that 70% of the items advertised in its classifieds section are sold
within 1 week of the first appearance of the ad. To check the validity of the claim, the
newspaper randomly selected n = 25 advertisements from last year’s classifieds and
contacted the people who placed the ads. They found that 14 of the 25 items sold within a
week. Based on the newspaper’s claim, is it likely to observe x 14 who sold their item
within a week?
3)
4) Sales of a new line of athletic footwear are crucial to the success of a newly formed
company. The company wishes to estimate the average weekly sales of the new footwear
to within $150 with 99% reliability. The initial sales indicate that the standard deviation of
the weekly sales figures is approximately $1550. How many weeks of data must be
sampled for the company to get the information it desires?
4)
5) The scores on a standardized test are reported by the testing agency to have a mean of 70.
Based on his personal observations, a school guidance counselor believes the mean score is
much higher. He collects the following scores from a sample of 50 randomly chosen
students who took the test.
5)
39
71
79
85
90
48
71
79
86
91
55
73
79
86
92
63
74
80
88
92
66
76
80
88
93
68
76
82
88
95
68
76
83
88
96
69
77
83
89
97
70
78
83
89
97
71
79
85
89
99
Use the data to conduct a test of hypotheses at = .05 to determine whether there is any
evidence to support the counselor’s suspicions.
6) One year, the distribution of salaries for professional sports players had mean $1.6 million
and standard deviation $0.8 million. Suppose a sample of 400 major league players was
taken. Find the approximate probability that the average salary of the 400 players that year
exceeded $1.1 million.
6)
7) The table shows the number of each type of book found at an online auction site during a
recent search.
7)
Type of Book
Children’s
Fiction
Nonfiction
Educational
Number
51,033
141,114
253,074
67,252
a. Construct a relative frequency table for the book data.
b. Construct a pie chart for the book data.
2
8) An ink cartridge for a laser printer is advertised to print an average of 10,000 pages. A
random sample of eight businesses that have recently bought this cartridge are asked to
report the number of pages printed by a single cartridge. The results are shown.
9771
9975
9811
10,079
9885
10,145
8)
9914
10,214
Assume that the data belong to a normal population. Test the null hypothesis that the
mean number of pages is 10,000 against the alternative hypothesis µ 10,000. Use = .10.
9) Three companies (A, B, and C) are to be ranked first, second, and third in a list of
companies with the highest customer satisfaction.
9)
a. List all the possible sets of rankings for these top three companies.
b. Assuming that all sets of rankings are equally likely, what is the probability that
Company A will be ranked first, Company B second, and Company C third?
c. Assuming that all sets of rankings are equally likely, what is the probability that
Company B will be ranked first?
10)
10)
For the distribution drawn here, identify the mean, median, and mode.
11) A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random
sample of 70 adults over 50, what is the mean and standard deviation of the number who
wear glasses?
3
11)
12) The overnight shipping business has skyrocketed in the last ten years. The single greatest
predictor of a company’s success is customer service. A study was conducted to determine
the customer satisfaction levels for one overnight shipping business. In addition to the
customer’s satisfaction level, the customers were asked how often they used overnight
shipping. The results are shown below in the following table:
Frequency of Use
< 2 per month 2 - 5 per month > 5 per month
TOTAL
High
250
140
70
460
Satisfaction level
Medium
140
55
25
220
Low
10
5
5
20
12)
TOTAL
400
200
100
700
A customer is chosen at random. Given that the customer uses the company two to five
times per month, what is the probability that the customer expressed low satisfaction with
the company?
13) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog
feeding by a lake in the 15 minute period following the addition of food. The data showing
the number of grunts and and the age of the warthog (in days) are listed below:
Number of Grunts
90
68
39
44
63
40
62
17
20
13)
Age (days)
125
141
155
160
167
174
183
189
195
Find and interpret the value of r.
14) The data below show the age and favorite type of music of 779 randomly selected people.
Test the claim that age and preferred music type are independent. Use = 0.05.
Age
Country Rock Pop Classical
15 – 21
21
45
90
33
21 – 30
68
55
42
48
30 – 40
65
47
31
57
40 – 50
60
39
25
53
4
14)
15) A random sample of 50 employees of a large company was asked the question, “Do you
participate in the company’s stock purchase plan?” The answers are shown below.
yes
no
no
yes
no
no
yes
yes
no
yes
no
yes
yes
no
yes
yes
yes
no
yes
no
no
no
yes
yes
yes
no
yes
yes
yes
yes
yes
no
no
yes
yes
yes
no
yes
yes
yes
no
yes
yes
no
yes
15)
no
yes
yes
yes
yes
Use a 90% confidence interval to estimate the proportion of employees who participate in
the company’s stock purchase plan.
16) To help consumers assess the risks they are taking, the Food and Drug Administration
(FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A
new cigarette has recently been marketed. The FDA tests on this cigarette yielded a mean
nicotine content of 25.9 milligrams and standard deviation of 2.7 milligrams for a sample
of n = 95 cigarettes. Find a 95% confidence interval for µ.
16)
17) Each year advertisers spend billions of dollars purchasing commercial time on network
television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the
largest spenders? In a recent article, the top 10 leading spenders and how much each spent
(in million of dollars) were listed:
17)
Company A
Company B
Company C
Company D
Company E
$72
63.6
57.3
54
31.1
Company F $27.3
Company G
25
Company H 23.8
Company I
23.1
Company J
19.2
Calculate the sample variance.
18) Farmers often sell fruits and vegetables at roadside stands during the summer. One such
roadside stand has a daily demand for tomatoes that is approximately normally
distributed with a mean of 128 tomatoes and a standard deviation of 30 tomatoes. How
many tomatoes must be available on any given day so that there is only a 1.5% chance that
all tomatoes will be sold?
18)
19) The following data represent the scores of 50 students on a statistics exam. The mean score
is 80.02, and the standard deviation is 11.9.
19)
39
71
79
85
90
51
71
79
86
90
59
73
79
86
91
63
74
80
88
91
66
76
80
88
92
68
76
82
88
95
68
76
83
88
96
69
77
83
89
97
70
78
83
89
97
71
79
85
89
98
What percentage of the scores lies within one standard deviation of the mean? two
standard deviations of the mean? three standard deviations of the mean? Based on these
percentages, do you believe that the distribution of scores is mound-shaped and
symmetric? Explain.
5
20) The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8.
Construct a 95% confidence interval for the population mean µ.
6
20)