Download Test 4 review - Middle Tennessee State University

test 4 review 1010
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Find the area under the normal curve for the condition.
7) Find the percent of the area under the curve
between the mean and 3.01 standard
deviations from the mean.
Use the given data to construct a frequency and relative
frequency distribution.
1) Kevin asked some of his friends how many
hours they had worked during the previous
week at their after-school jobs. The results are
shown below.
6
5
5 6 4
8 6 5
6 6
8 6
9
5
Use the standard normal curve table to find the closest
z-score for the given condition.
8) 74.9% of the total area is to the left of z.
A company installs 5,000 light bulbs. The lifetimes of the
lightbulbs are approximately normally distributed with a
mean of 500 hours and a standard deviation of 100 hours.
Find the approximate number of bulbs that can be
expected to last the indicated amount of time.
9) More than 740 hours
8 6 4 8 5
8 5 8 8 4
Construct a frequency and relative frequency
distribution. Use 4 classes.
Find the mean of the set of data.
2)
3.5 1.6 2.4 3.7 4.1
3.9 1.0 3.6 4.2 3.4
3.7 2.2 1.5 4.2 3.4
2.7 0.4 3.7 2.0 3.6
Find the indicated probability or percentage for the
normally distributed variable.
10) A machine produces pencils with a mean
diameter of 0.30 inches and a standard
deviation of 0.01 inches. The diameters are
approximately normally distributed. What is
the probability that a randomly selected pencil
has a diameter less than 0.285 inches?
Round your answer to two decimal places.
Find the range for the set of data given.
3) 117 527 136 607 404
Solve the problem.
11) Scores on a test are approximately normally
distributed with a mean of 70 and a standard
deviation of 9. The teacher wants to give A's to
the top 10% of students, B's to the next 25%,
and C's to the next 42%. What is the bottom
cutoff for a C grade? Round your answer to the
nearest whole number.
237
Solve the problem.
4) At Loop Junior College, the mean grade point
average (gpa) of the current student body is
2.76 with a standard deviation of 0.64.
Compute the gpa's of each student to two
decimal places.
12) At Loop College, the mean grade point
average (gpa) of the current student body is
2.76 with a standard deviation of 0.64. Find the
gpa of a student whose z-score is -2.8. Round
A gpa with a z-score of 0.6.
A gpa with a z-score of -1.2.
Classify the random variable as either discrete or
continuous.
5) The number of colleges in a state
to the nearest hundredth.
Rank the data from lowest to highest and determine the
requested quartile.
13) The following scores on the midterm exam in
Chemistry 102 were recorded.
At one high school, the mean time for running the
100-yard dash is 15.2 seconds with a standard deviation of
0.9 seconds. The times are very closely approximated by a
normal curve. Find the percent of times that are:
6) Between 15.2 and 16.1 seconds
93 81 59 69 82 74 61 77 95 84 88 71
85 97 63 72 89 80 60 98 91 62 78 83
76 81 94 66 83 96
Find the 1st quartile, Q1 .
1
Find the indicated decile or percentile.
14) The test scores of 19 students are listed below.
Find the sixth decile, D6 .
36
56
68
88
45
59
70
91
49
61
74
92
Provide an appropriate response.
20) We want to compare two different groups of
students, students taking Composition 1 in a
traditional lecture format and students taking
Composition 1 in a distance learning format.
We know that the mean score on the research
paper is 85 for both groups. What additional
information would be provided by knowing
the standard deviation?
53 55
62 65
78 84
99
Solve.
Find the median.
21) 31, 14, 7, 5, 24, 12, 29, 31, 40, 35
15)
Find the mode or modes.
22) 7.07, 7.41, 7.56, 7.07, 7.88, 7.99, 7.62
Give the median of the data set represented by
the box plot above.
Find the mean for the given frequency distribution.
23)
Value Frequency
12
2
17
12
22
20
31
13
33
10
True or false?
16) A person who scored at the eightieth percentile
in a test answered eighty percent of the
questions correctly.
Find the standard deviation. Round to one more place than
the data.
17) 2, 3, 16, 18, 6, 19, 11, 18, 17
Find the median for the given frequency distribution.
Value Frequency
60 4
62 8
24) 64 12
66 20
68 31
70 13
Use Chebyshev's theorem to solve the problem.
18) In a certain distribution of numbers, the mean
is 50 and the standard deviation is 6. What can
you say about the percentage of numbers that
lie between 29 and 71?
Find the mean for the given sample data. Unless otherwise
specified, round your answer to one more decimal place
than that used for the observations.
25) Last year, nine employees of an electronics
company retired. Their ages at retirement are
listed below. Find the mean retirement age.
Find the standard deviation for the given data. Round
your final answer to one more decimal place than that
used for the observations.
19) Christine is currently taking college
astronomy. The instructor often gives quizzes.
On the past seven quizzes, Christine got the
following scores.
51 20
114 25
10
46
56 67
55 68
61 50
58
2
63
58
54
Find the median for the given sample data.
26) The weights (in ounces) of 21 cookies are
shown. Find the median weight.
Construct a frequency polygon.
30)
Number of
Number of
vacation days employees
1-5
10
6-10
25
11-15
35
16-20
20
21-25
10
0.72 1.26 0.80 1.62 0.86 0.60 1.09
1.26 1.53 0.95 0.72 1.45 1.03 0.80
0.47 1.45 0.60 1.03 1.72 0.86 0.56
Solve the problem.
27) Jackie's sisters weigh 117 lb, 148 lb, 128 lb, and
125 lb. The average female in her city weighs
139.1 lb. How much does Jackie weigh if she
and her sisters have an average weight of 139.1
lb?
Provide an appropriate response.
28) The median of a data set is
always/sometimes/never (select one) one of the
data points in a set of data. Explain your
answer with brief examples.
Construct a stem and leaf display for given data.
31) Mr. Johnson wants to display his employees'
ages in a graph. Below are their ages.
23 36 45
42 34 53
34 27 24
Construct the specified histogram.
29) The ages of the voters at a poll during a
20-minute period are listed below. Use five
classes with a uniform width of 10 years,
where the lower limit of the first class is 20
years.
Use this graph to answer the question.
Big "D" Sales for 2009, 2010
35 29 48 63 64 38 21 23 41 68
61 42 43 47 33 37 46 27 23 30
Sales
(thousands of dollars)
2010
2009
Month
32) What month in 2010 had the lowest sales?
3
Answer the question.
33) The bar graph below shows the number of
students by major in the College of Arts and
Sciences.
In a school survey, students showed these preferences for
instructional materials. Answer the question.
35) How many degrees are in the central angle for
the "Lecture" sector?
MAJOR
Use the information to complete a circle graph. Note that
the circle is divided into 100 equal sections.
36) Main form of exercise for employees of one
company:
None:
30%
Walking:
18%
Running:
4%
Golf:
11%
Weight Training:
26%
Other:
11%
Did twice as many students major in English
as in Math?
This double-bar graph shows the number of male (M) and
female (F) athletes at a university over a four-year period.
Answer the question.
YEAR
34) Which year had the smallest number of female
athletes?
4
Use the graph to answer the question.
37)
Make a bar graph to represent the data.
40) Construct a vertical bar graph for the relative
frequencies given.
Blood
type
O
A
B
AB
Frequency
22
19
6
3
Relative
frequency
0.44
0.38
0.12
0.06
Mike decides to buy shares of companies A, B,
and C, which were initially selling for the same
price. The changes in each stock's value are
shown in the graph above. At its peak, stock A
was valued at approximately how much more
than either B or C?
Provide an appropriate response.
41) Shortly before a mayoral election, a market
research firm took a poll to find out which
candidate people were planning to vote for.
The results are shown below.
Solve the problem.
38) Sixteen workers were surveyed about how
long it takes them to travel to work each day.
The data below are given in minutes.
Represent the data in a double-stem display.
20 35 42 20 24 37 23 24
22 20 41 25 28 27 30 32
Candidate
Li Fong
Bob Green
Sue Moore
Jose Alvarez
Find the indicated probability.
39) A relative frequency distribution is given
below for the size of families in one U.S. city.
Size
2
3
4
5
6
7+
Frequency
2120
2329
1042
399
You wish to construct a graph to represent the
data. It should be easy to see from your graph
which candidate is in the lead. Which graph
would be more useful, a bar graph or a pie
chart? Explain your thinking.
Relative frequency
0.448
0.208
0.203
0.094
0.029
0.018
A family is selected at random. Find the
probability that the size of the family is
between 2 and 5 inclusive. Round your answer
to three decimal places.
5
Answer Key
Testname: UNTITLED1
1)
Hours Frequency Relative Frequency
x
f
f/n
3-4
3
3/24 ≈ 13%
5-6
13
13/24 ≈ 54%
7- 8
7
7/24 ≈ 29%
9-10
1
1/24 ≈ 4%
2) 2.94
3) 490
4) 3.14, 1.99
5) Discrete
6) 34%
7) 49.9%
8) 0.67
9) 40
10) 0.067
11) 63
12) 0.97
13) 71
14) 70
15) 35
16) False
17) 6.9
18) at least 91.8%
19) 34.7
20) Answers will vary. Possible answer: The standard deviation will give an indication of how widely the scores vary.
More precisely, it gives an indication of how much the scores deviate, on average, from the mean score of 85.
21) 26.5
22) 7.07
23) 24.6
24) 67
25) 59.1
26) 0.95 ounces
27) 177.5 lb
28) Answers will vary. Possible answer: The median is sometimes one of the data points. If the number of data points is
odd, the median will be one of the data points (the middle data point). If the number of data points is even, the
median is the average of the two middle data points which will be equal to one of the data points only if the two
middle data points are identical.
6
Answer Key
Testname: UNTITLED1
29)
30) Frequency
Number of vacation days
31)
2 347
3 446
4 25
53
32) Month 2
33) Yes
34) 1986
35) 64.8°
36)
37) $35
38)
(20-24)
(25-29)
(30-34)
(35-39)
(40-44)
39) 0.953
2
2
3
3
4
0002344
578
02
57
12
7
Answer Key
Testname: UNTITLED1
40)
41) Answers will vary. Possible answer: A bar graph would be more useful. A bar graph is useful for comparing the sizes
of different categories with each other, since it is easy to compare the heights of different bars.
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