Download Normal Distribution

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) Find the area of the indicated region under the standard normal curve.
A) 0.0823
B) 0.0968
C) 0.4032
1)
D) 0.9032
2) Find the area of the indicated region under the standard normal curve.
A) 0.0968
B) 0.0823
C) 0.9032
2)
D) 0.9177
3)
3) Find the area of the indicated region under the standard normal curve.
A) 0.309
B) 0.3438
C) 0.6562
D) 1.309
4)
4) Find the area of the indicated region under the standard normal curve.
A) 0.0212
B) 0.8489
C) 0.1504
D) 0.1292
5) Find the area under the standard normal curve to the left of z = 1.5.
A) 0.0668
B) 0.5199
C) 0.9332
D) 0.7612
6) Find the area under the standard normal curve to the left of z = 1.25.
A) 0.2318
B) 0.8944
C) 0.7682
D) 0.1056
1
5)
6)
7) Find the area under the standard normal curve to the right of z = 1.
A) 0.8413
B) 0.1397
C) 0.1587
D) 0.5398
8) Find the area under the standard normal curve to the right of z = -1.25.
A) 0.6978
B) 0.7193
C) 0.5843
D) 0.8944
7)
8)
9) Find the area under the standard normal curve between z = 0 and z = 3.
A) 0.0010
B) 0.4641
C) 0.4987
D) 0.9987
10) Find the area under the standard normal curve between z = 1 and z = 2.
A) 0.8413
B) 0.5398
C) 0.2139
D) 0.1359
11) Find the area under the standard normal curve between z = -1.5 and z = 2.5.
A) 0.9270
B) 0.9831
C) 0.6312
D) 0.7182
12) Find the area under the standard normal curve between z = 1.5 and z = 2.5.
A) 0.9938
B) 0.9332
C) 0.0606
D) 0.9816
9)
10)
11)
12)
13) Find the area under the standard normal curve between z = -1.25 and z = 1.25.
A) 0.6412
B) 0.2112
C) 0.8817
D) 0.7888
13)
14) Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right
of z = 1.25.
A) 0.7888
B) 0.1056
C) 0.3944
D) 0.2112
14)
15) Find the area of the indicated region under the standard normal curve.
15)
A) 0.0968
B) 0.0823
C) 0.4032
D) 0.9032
16)
16) Find the area of the indicated region under the standard normal curve.
A) 0.9032
B) 0.0968
C) 0.9177
2
D) 0.0823
17)
17) Find the area of the indicated region under the standard normal curve.
A) 0.309
B) 1.309
C) 0.3438
D) 0.6562
18)
18) Find the area of the indicated region under the standard normal curve.
A) 0.8489
B) 0.1292
C) 0.1504
D) 0.0212
19) Find the area under the standard normal curve to the left of z = 1.5.
A) 0.7612
B) 0.5199
C) 0.9332
D) 0.0668
19)
20) Find the area under the standard normal curve to the left of z = 1.25.
A) 0.2318
B) 0.8944
C) 0.7682
D) 0.1056
21) Find the area under the standard normal curve to the right of z = 1.
A) 0.8413
B) 0.1397
C) 0.1587
D) 0.5398
22) Find the area under the standard normal curve to the right of z = -1.25.
A) 0.8944
B) 0.7193
C) 0.6978
D) 0.5843
20)
21)
22)
23) Find the area under the standard normal curve between z = 0 and z = 3.
A) 0.4987
B) 0.4641
C) 0.0010
D) 0.9987
24) Find the area under the standard normal curve between z = 1 and z = 2.
A) 0.8413
B) 0.2139
C) 0.1359
D) 0.5398
25) Find the area under the standard normal curve between z = -1.5 and z = 2.5.
A) 0.6312
B) 0.7182
C) 0.9831
D) 0.9270
26) Find the area under the standard normal curve between z = 1.5 and z = 2.5.
A) 0.9332
B) 0.9938
C) 0.0606
23)
24)
25)
26)
D) 0.9816
27) Find the area under the standard normal curve between z = -1.25 and z = 1.25.
A) 0.2112
B) 0.7888
C) 0.6412
D) 0.8817
27)
28) Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right
of z = 1.25.
A) 0.2112
B) 0.7888
C) 0.3944
D) 0.1056
28)
3
Find the probability of z occurring in the indicated region.
29)
0 1.82
A) 0.9772
29)
z
B) 0.0344
C) 0.4656
D) 0.9656
30)
30)
-0.59
0
A) 0.7224
z
B) 0.2776
C) 0.2224
D) 0.1894
31)
31)
-1.33
A) 0.0918
z
0
B) 0.9082
C) 0.0668
4
D) 0.9332
32)
32)
0
A) 0.0228
1.75
z
B) 0.9599
C) 0.0401
D) 0.0668
33)
33)
-2 0
A) 0.0228
3
z
B) 0.0456
C) 0.9772
D) 0.9544
34)
34)
0
A) 0.4332
1.50
z
B) 0.0668
C) 0.5668
5
D) 0.9332
Provide an appropriate response.
35) Use the standard normal distribution to find P(0 < z < 2.25).
A) 0.4878
B) 0.7888
C) 0.8817
D) 0.5122
36) Use the standard normal distribution to find P(-2.25 < z < 0).
A) 0.0122
B) 0.6831
C) 0.5122
D) 0.4878
37) Use the standard normal distribution to find P(-2.25 < z < 1.25).
A) 0.8944
B) 0.8822
C) 0.4878
D) 0.0122
38) Use the standard normal distribution to find P(-2.50 < z < 1.50).
A) 0.6167
B) 0.9270
C) 0.8822
D) 0.5496
39) Use the standard normal distribution to find P(z < -2.33 or z > 2.33).
A) 0.7888
B) 0.0606
C) 0.0198
D) 0.9802
35)
36)
37)
38)
39)
40) For the standard normal curve, find the z-score that corresponds to the third quartile.
A) 0.67
B) 0.77
C) -0.23
D) -0.67
40)
41) For the standard normal curve, find the z-score that corresponds to the first quartile.
A) -0.23
B) 0.77
C) 0.67
D) -0.67
41)
42) For the standard normal curve, find the z-score that corresponds to the first decile.
A) 1.28
B) -2.33
C) -1.28
D) 0.16
42)
Provide an appropriate response. Use the Standard Normal Table to find the probability.
43) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An
individualʹs IQ score is found to be 110. Find the z-score corresponding to this value.
A) 0.67
B) -1.33
C) -0.67
D) 1.33
43)
44) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An
individualʹs IQ score is found to be 90. Find the z-score corresponding to this value.
A) -0.67
B) 1.33
C) -1.33
D) 0.67
44)
45) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An
individualʹs IQ score is found to be 120. Find the z-score corresponding to this value.
A) -1.33
B) 0.67
C) 1.33
D) -0.67
45)
46) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
IQ score that corresponds to a z-score of 1.96.
A) 115.6
B) 129.4
C) 132.1
D) 122.4
46)
47) IQ test scores are normally distributed with a mean of 102 and a standard deviation of 19. An
individualʹs IQ score is found to be 124. Find the z-score corresponding to this value.
A) -0.86
B) 1.16
C) 0.86
D) -1.16
47)
48) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 12. An
individualʹs IQ score is found to be 127. Find the z-score corresponding to this value.
A) 2.25
B) 0.44
C) -0.44
D) -2.25
48)
6
49) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a
standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days.
A) 0.0166
B) 0.9834
C) 0.3189
D) 0.2375
49)
50) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a
standard deviation of 15 days. Find the probability of a pregnancy lasting less than 250 days.
A) 0.0066
B) 0.0606
C) 0.1151
D) 0.1591
50)
51) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and
σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find
the probability that a teenage boy has a cholesterol level greater than 200.
A) 0.8413
B) 0.1587
C) 0.3419
D) 0.2138
51)
52) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and
σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find
the probability that a teenage boy has a cholesterol level greater than 225.
A) 0.0606
B) 0.0336
C) 0.0012
D) 0.0718
52)
53) An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose less than 20 suitcases?
A) 0.8944
B) 0.4040
C) 0.3944
D) 0.1056
53)
54) An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose more than 20 suitcases?
A) 0.3944
B) 0.1056
C) 0.4040
D) 0.8944
54)
55) An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose between 10 and 20 suitcases?
A) 0.1056
B) 0.4040
C) 0.3944
D) 0.8314
55)
56) Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at
random, find the probability that he or she makes more than $36,000.
A) 0.9082
B) 0.1056
C) 0.4040
D) 0.0918
56)
57) Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at
random, find the probability that he or she makes less than $28,000.
A) 0.0918
B) 0.9827
C) 0.2113
D) 0.9981
57)
58) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a
standard deviation of 2.5 inches. The cheerleaders for a local professional basketball team must be
between 65.5 and 68.0 inches. If a woman is randomly selected, what is the probability that her
height is between 65.5 and 68.0 inches?
A) 0.7881
B) 0.1844
C) 0.9608
D) 0.3112
58)
7
59) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a
standard deviation of 15 days. A baby is premature if it is born three weeks early. What percent of
babies are born prematurely?
A) 8.08%
B) 9.21%
C) 6.81%
D) 10.31%
59)
60) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and
σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention.
What percent of teenage boys have levels between 170 and 225?
A) 3.36%
B) 46.64%
C) 56.13%
D) 6.06%
60)
61) Assume that blood pressure readings are normally distributed with μ = 120 and σ = 8. A blood
pressure reading of 145 or more may require medical attention. What percent of people have a
blood pressure reading greater than 145?
A) 99.91%
B) 0.09%
C) 11.09%
D) 6.06%
61)
62) Assume that the heights of American men are normally distributed with a mean of 69.0 inches and
a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between
64 and 78 inches. Find the percent of men meeting these height requirements.
A) 96.26%
B) 31.12%
C) 99.93%
D) 3.67%
62)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
63) Assume that the heights of women are normally distributed with a mean of 63.6 inches
and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women
be between 58 and 80 inches. If a woman is randomly selected, what is the probability that
her height is between 58 and 80 inches?
63)
64) The lengths of pregnancies are normally distributed with a mean of 268 days and a
standard deviation of 15 days. Out of 50 pregnancies, how many would you expect to last
less than 250 days?
64)
65) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170
and σ = 30. Levels above 200 warrant attention. If 95 teenage boys are examined, how
many would you expect to have cholesterol levels greater than 225?
65)
66) An airline knows from experience that the distribution of the number of suitcases that get
lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. In
one year, how many weeks would you expect the airline to lose between 10 and 20
suitcases?
66)
67) Assume that the heights of women are normally distributed with a mean of 63.6 inches
and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women
be between 58 and 80 inches. If 200 women want to enlist in the U.S. Army, how many
would you expect to meet the height requirements?
67)
68) Assume that the heights of men are normally distributed with a mean of 69.0 inches and a
standard deviation of 2.8 inches. The U.S. Marine Corps requires that the heights of men
be between 64 and 78 inches. If 500 men want to enlist in the U.S. Marine Corps, how
many would you not expect to meet the height requirements?
68)
8
Provide an appropriate response.
69) Find the z-score that corresponds to the given area under the standard normal curve.
69)
70) Find the z-score that corresponds to the given area under the standard normal curve.
70)
71) Find the z-score that corresponds to the given area under the standard normal curve.
71)
72) Find the z-score that corresponds to the given area under the standard normal curve.
72)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
73) Find the z-scores for which 90% of the distributionʹs area lies between -z and z.
A) (-0.99, 0.99)
B) (-1.645, 1.645)
C) (-1.96, 1.96)
D) (-2.33, 2.33)
73)
74) Find the z-scores for which 98% of the distributionʹs area lies between -z and z.
A) (-0.99, 0.99)
B) (-1.645, 1.645)
C) (-1.96, 1.96)
D) (-2.33, 2.33)
74)
75) Find the z-score for which 70% of the distributionʹs area lies to its right.
A) -0.81
B) -0.47
C) -0.53
75)
D) -0.98
76) Find the z-score that is greater than the mean and for which 70% of the distributionʹs area lies to
its left.
A) 0.47
B) 0.81
C) 0.53
D) 0.98
9
76)
77) Use a standard normal table to find the z -score that corresponds to the cumulative area of 0.7019.
A) -0.53
B) 0.835
C) 0.53
D) -0.835
77)
78) Find the z-score that has 93.82% of the distributionʹs area to its right.
A) -1.54
B) 0.155
C) -0.155
78)
D) 1.54
79) Find the z-score for which 99% of the distributionʹs area lies between -z and z.
B) (-2.33, 2.33)
C) (-1.645, 1.645)
D) (-1.96, 1.96)
A) (-2.575, 2.575)
79)
80) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
x-score that corresponds to a z-score of 2.33.
A) 134.95
B) 139.55
C) 142.35
D) 125.95
80)
81) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
x-score that corresponds to a z-score of -1.645.
A) 82.3
B) 91.0
C) 75.3
D) 79.1
81)
82) The scores on a mathematics exam have a mean of 77 and a standard deviation of 8. Find the
x-value that corresponds to the z-score 2.575.
A) 56.4
B) 79.6
C) 97.6
D) 85.0
82)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
83) A mathematics professor gives two different tests to two sections of his college algebra
courses. The first class has a mean of 56 with a standard deviation of 9 while the second
class has a mean of 75 with a standard deviation of 15. A student from the first class scores
a 62 on the test while a student from the second class scores an 83 on the test. Compare the
scores.
83)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
84) Compare the scores: a score of 75 on a test with a mean of 65 and a standard deviation of 8 and a
score of 75 on a test with a mean of 70 and a standard deviation of 4.
A) A score of 75 with a mean of 70 and a standard deviation of 4 is better.
B) The two scores are statistically the same.
C) You cannot determine which score is better from the given information.
D) A score of 75 with a mean of 65 and a standard deviation of 8 is better.
84)
85) Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a
mean of 70.
A) You cannot determine which score is better from the given information.
B) The two scores are statistically the same.
C) A score of 75 with a mean of 70 and a standard deviation of 4 is better.
D) A score of 75 with a mean of 65 and a standard deviation of 8 is better.
85)
86) Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and
a score of 90 on a test with a mean of 80 and a standard deviation of 8.
A) You cannot determine which score is better from the given information.
B) A score of 220 with a mean of 200 and a standard deviation of 21 is better.
C) The two scores are statistically the same.
D) A score of 90 with a mean of 80 and a standard deviation of 8 is better.
86)
10
87) Two high school students took equivalent language tests, one in German and one in French. The
student taking the German test, for which the mean was 66 and the standard deviation was 8,
scored an 82, while the student taking the French test, for which the mean was 27 and the standard
deviation was 5, scored a 35. Compare the scores.
A) A score of 35 with a mean of 27 and a standard deviation of 5 is better.
B) The two scores are statistically the same.
C) A score of 82 with a mean of 66 and a standard deviation of 8 is better.
D) You cannot determine which score is better from the given information.
87)
88) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8
and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the
SAT and 25 on the ACT. Compare the scores.
A) You cannot determine which score is better from the given information.
B) The two scores are statistically the same.
C) A score of 1130 on the SAT test was better.
D) A score of 25 on the ACT test was better.
88)
89) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8
and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the
SAT and 16 on the ACT. Compare the scores.
A) A score of 860 on the SAT test was better.
B) You cannot determine which score is better from the given information.
C) A score of 16 on the ACT test was better.
D) The two scores are statistically the same.
89)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
90) Assume that blood pressure readings are normally distributed with μ = 111 and σ = 7. A
researcher wishes to select people for a study but wants to exclude the top and bottom 10
percent. What would be the upper and lower readings to qualify people to participate in
the study?
90)
91) Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $32,000 and a standard deviation of $4000. What is the cutoff
salary for teachers in the top 10%?
91)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
92) Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $28,000 and a standard deviation of $3000. What is the cutoff salary for
teachers in the bottom 10%?
A) $23,065
B) $32,935
C) $31,840
D) $24,160
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
93) The times for completing one circuit of a bicycle course are normally distributed with a
mean of 64.5 minutes and a standard deviation of 7.8 minutes. An association wants to
sponsor a race but will cut the bottom 25% of riders. In a trial run, what should be the
cutoff time?
11
93)
92)
94) Assume that the heights of men are normally distributed with a mean of 70.6 inches and a
standard deviation of 2.2 inches. If the top 5 percent and bottom 5 percent are excluded for
an experiment, what are the cutoff heights to be eligible for this experiment? Round your
answers to one decimal place.
94)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
95) Assume that the heights of women are normally distributed with a mean of 63.5 inches and a
standard deviation of 2.5 inches. Find Q3 , the third quartile that separates the bottom 75% from the
top 25%.
A) 61.8
B) 66.4
C) 66.7
95)
D) 65.2
96) The body temperatures of adults are normally distributed with a mean of 98.6 ° F and a standard
deviation of 0.19° F. What temperature represents the 95th percentile?
A) 98.29° F
B) 98.91° F
C) 98.84° F
D) 98.97° F
96)
97) In a certain normal distribution, find the standard deviation σ when μ = 50 and 10.56% of the area
lies to the right of 55.
A) 5
B) 4
C) 3
D) 2
97)
98) In a certain normal distribution, find the mean μ when σ = 5 and 5.48% of the area lies to the left of
78.
A) 94
B) 70
C) 86
D) 62
98)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
99) In a certain normal distribution, 6.3% of the area lies to the left of 36 and 6.3% of the area
lies to the right of 42. Find the mean μ and the standard deviation σ.
99)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
100) A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of
48,400 miles and a standard deviation of 5000 miles. If the manufacturer is willing to replace no
more than 10% of the tires, what should be the approximate number of miles for a warranty?
A) 42,000
B) 40,175
C) 56,625
D) 54,800
12
100)
Answer Key
Testname: MATH211_NORMAL_DISTR
1) B
2) C
3) C
4) C
5) C
6) B
7) C
8) D
9) C
10) D
11) A
12) C
13) D
14) D
15) A
16) A
17) D
18) C
19) C
20) B
21) C
22) A
23) A
24) C
25) D
26) C
27) B
28) A
29) D
30) B
31) B
32) C
33) C
34) A
35) A
36) D
37) B
38) B
39) C
40) A
41) D
42) C
43) A
44) A
45) C
46) B
47) B
48) A
49) A
50) C
13
Answer Key
Testname: MATH211_NORMAL_DISTR
51) B
52) B
53) A
54) B
55) D
56) D
57) A
58) B
59) A
60) A
61) B
62) A
63) If x = 58, then z = -2.24 and P(x) = 0.0125. If x = 80, then z = 6.56 and P(x) = 0.9999. P(58 < x < 80) = 0.9999 - 0.0125 = 0.9874.
64) About 6 pregnancies
65) About 3 teenage boys
66) About 43 weeks
67) About 197 women
68) About 19 men
69) z = -0.58
70) z = -1.71
71) z = 0.42
72) z = 3.07
73) B
74) D
75) C
76) C
77) C
78) A
79) A
80) A
81) C
82) C
83) z = (62 - 56)/9 = 0.667; z = (83 - 75)/15 = 0.533. The student with the score of 62 has the better score.
84) B
85) A
86) D
87) C
88) D
89) A
90) (102.0, 120.0)
91) x = μ + zσ = 32,000 + (1.28)(4000) = $37,120
92) D
93) x = μ + zσ = 64.5 + (0.675)(7.8) = 69.77
94) 67.0 inches, 74.2 inches
95) D
96) B
97) B
98) C
99) μ = 39, σ = 1.96
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Answer Key
Testname: MATH211_NORMAL_DISTR
100) A
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