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Chapter 5 Review
The Normal Probability and Standardization
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) Approximately ____% of the area under the normal curve is between μ - σ and μ + σ.
A) 99.7
B) 95
C) 68
1)
D) 50
A random variable X is normally distributed with μ = 60. Convert the value of X to a z-score, if the standard deviation is
as given.
2) X = 72; σ = 3
A) 3
2)
B) 5
C) 12
D) 4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the standard normal-curve area indicated.
3) Between z = -1.3 and z = -0.4
3)
4) To the left of z = 0.67
4)
The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12
ounces and a standard deviation of 4 ounces.
5) Find the probability that more than 16 ounces is dispensed in a cup.
5)
6) Find the probability that between 15 and 18 ounces are dispensed in a cup.
6)
7) Find the number of ounces above which 80% of the dispensed sodas will fall. Round to the
nearest tenth.
7)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
A random variable X is normally distributed with μ = 60. Convert the value of X to a z-score, if the standard deviation is
as given.
8) X = 30; σ = 8
A) -8
8)
B) -3.75
C) 3.75
1
D) 8
Obtain the shaded area under the standard normal curve.
9)
9)
-2.34
-1.17
A) 0.7580
1.17
2.34 z
B) 0.2420
C) 0.8790
D) 0.1210
10)
10)
-2.31
2.31
A) 0.0208
B) 0.9896
z
C) 0.0104
D) 0.9792
11)
11)
-1.76
-0.88
A) 0.3788
0.88
1.76
z
B) 0.1894
C) 0.6212
D) 0.8106
find the required z-score.
12) Find the z-score for which the area under the standard normal curve to its left is 0.96
A) 1.03
B) -1.38
C) 1.75
12)
D) 1.82
13) Find the z-score having area 0.86 to its right under the standard normal curve; that is, find z
.
13)
14) Scores on a standardized test are normally distributed with a mean of 96 and a standard deviation
of 12. An individual's test score is found to be 128. Find the z-score corresponding to this value.
14)
A) 1.08
B) -1.08
C) 0.8051
0.86
D) 0.5557
Provide an appropriate response.
A) -0.37
B) -2.67
C) 0.38
2
D) 2.67
find the required z-score.
15) Determine the two z-scores that divide the area under the standard normal curve into a middle
0.96 area and two outside 0.02 areas.
A) 0 and 2.05
B) -1.75 and 1.75
C) -2.05 and 2.05
15)
D) -2.33 and 2.33
Provide an appropriate response.
16) Find the z-scores for which 98% of the distribution's area lies between -z and z.
A) (-1.96, 1.96)
B) (-0.99, 0.99)
C) (-2.33, 2.33)
16)
D) (-1.645, 1.645)
17) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 302 seconds.
A) 0.4893
B) 0.9893
C) 0.0107
D) 0.5107
18) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 470 seconds and a standard deviation of 50 seconds. Find the probability that a randomly
selected boy in secondary school will take longer than 355 seconds to run the mile.
A) 0.0107
B) 0.9893
C) 0.5107
B) 0.2674
C) 0.3551
B) 0.2266
C) 0.8413
20)
D) 0.7266
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
21) A firm believes the internal rate of return for its proposed investment can best be described
by a normal distribution with mean 20% and standard deviation 3%. What is the
probability that the internal rate of return for the investment will be at least 15.5%?
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19)
D) 0.3085
20) The tread life of a particular brand of tire is a random variable best described by a normal
distribution with a mean of 60,000 miles and a standard deviation of 2500 miles. What is the
probability a particular tire of this brand will last longer than 57,500 miles?
A) 0.1587
18)
D) 0.4893
19) The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 6.5 minutes and a standard deviation of 1 minute. Find the
probability that a randomly selected college student will find a parking spot in the library parking
lot in less than 6.0 minutes.
A) 0.1915
17)
21)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
22) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize
the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat
in order to earn a certificate of recognition from the fitness association?
A) 367.75 sec
B) 386 sec
C) 514 sec
D) 532.25 sec
23) The amount of corn chips dispensed into a 16-ounce bag by the dispensing machine has been
identified as possessing a normal distribution with a mean of 16.5 ounces and a standard deviation
of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight distribution?
A) 16.63 oz
B) 16.13 oz
C) 16.09 oz
B) 5.0 min
C) 4.8 min
23)
D) 16.59 oz
24) The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the
cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the
library parking lot.
A) 5.3 min
22)
24)
D) 5.2 min
Solve the problem.
25) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric
energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill
of a 3-bedroom house using gas or electric energy had a mean of $115 and a standard deviation of
$12. Three solar homes reported monthly utility bills of $75, $74, and $77. Which of the following
statements is true?
A) Homes using solar power may have lower utility bills than homes using only gas and
electricity.
B) The utility bills for homes using solar power are about the same as those for homes using only
gas and electricity.
C) Homes using solar power always have lower utility bills than homes using only gas and
electricity.
D) Homes using solar power may actually have higher utility bills than homes using only gas
and electricity.
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25)
26) On a given day, gasoline prices in the state of Colorado had a mean price of $2.20/gallon with a
standard deviation of $0.09. A particular Colorado gas station had gasoline for $2.11/gallon.
Interpret the z-score for this gas station.
26)
A) The gas price of this Colorado station falls 9 standard deviations above the mean gas price of
all Colorado stations.
B) The gas price of this station falls 1 standard deviation above the mean gas price of all
Colorado stations.
C) The gas price of this station falls 1 standard deviation below the mean gas price of all
Colorado stations.
D) The gas price of this Colorado station falls 9 standard deviations below the mean gas price of
all Colorado stations.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
27) Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores
for a physics class had a mean of 69 with a standard deviation of 3.7. One student earned
a 82 on the history test and a 84 on the physics test. Calculate the z-score for each test. On
which test did the student perform better?
27)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
28) The speeds of the fastballs thrown by major league baseball pitchers were measured by radar gun.
The mean speed was 88 miles per hour. The standard deviation of the speeds was 6 mph. Which of
the following speeds would be classified as an outlier?
A) 82 mph
B) 107 mph
C) 97 mph
28)
D) 76 mph
29) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits
during the tournament. The statistician reported that the mean serve speed of a particular player
was 98 miles per hour (mph) and the standard deviation of the serve speeds was 9 mph. Using the
z-score approach for detecting outliers, which of the following serve speeds would represent
outliers in the distribution of the player's serve speeds?
29)
Speeds: 67 mph, 107 mph, and 116 mph
A) 67 and 107 are both outliers, but 116 is not.
B) 67 is the only outlier.
C) 67, 107, and 116 are all outliers.
D) None of the three speeds is an outlier.
30) The mean x of a data set is 36.71, and the sample standard deviation s is 3.22. Find the interval
representing measurements within one standard deviation of the mean.
A) (33.49, 39.93)
B) (27.05, 46.37)
C) (35.71, 37.71)
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D) (30.27, 43.15)
30)
31) The following is a list of 25 measurements:
12
13
12
18
14
16
14
11
17
17
16
19
18
16
15
14
13
18
17
15
15
31)
17
14
11
19
How many of the measurements fall within one standard deviation of the mean?
A) 18
B) 13
C) 25
D) 16
32) A standardized test has a mean score of 500 points with a standard deviation of 100 points. Five
students' scores are shown below.
Adam: 575
Beth: 690
Carlos: 750 Doug: 280
32)
Ella: 440
Which of the students have scores within two standard deviations of the mean?
A) Adam, Beth, Carlos, Ella
B) Carlos, Doug
C) Adam, Beth
D) Adam, Beth, Ella
33) 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 16 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.
33)
A) between 12 and 20 hours per week
B) less than 20
C) less than 14 and more than 18 hours per week
D) between 10 and 22 hours per week
34) A study was designed to investigate the effects of two variables  (1) a student's level of
mathematical anxiety and (2) teaching method  on a student's achievement in a mathematics
course. Students who had a low level of mathematical anxiety were taught using the traditional
expository method. These students obtained a mean score of 380 with a standard deviation of 30 on
a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would
approximately 68% of the students score?
A) below 410
B) between 350 and 410
C) below 350 and above 410
D) above 410
35) The distribution of scores on a test is mound-shaped and symmetric with a mean score of 78. If
68% of the scores fall between 72 and 84, which of the following is most likely to be the standard
deviation of the distribution?
A) 12
B) 2
C) 6
6
D) 3
34)
35)
Answer Key
Testname: CH5REVIEW NORMAL DIST
1) C
2) D
3) 0.2478
4) 0.7486
5) 0.1587
6) 0.1598
7) 8.6 ounces
8) B
9) A
10) A
11) A
12) C
13) B
14) D
15) C
16) C
17) C
18) B
19) D
20) C
21) Let x be the internal rate of return. Then x is a normal random variable with μ = 20% and σ = 3%. To determine the
probability that x is at least 15.5%, we need to find the z-value for x = 15.5%.
x - μ 15.5 - 20
z=
=
= -1.5
σ
3
P(x ≥ 15.5%) = P(-1.5 ≤ z) = 0.5 + P(-1.5 ≤ z ≤ 0) = 0.5 + 0.4332 = 0.9332
22) B
23) D
24) D
25) A
26) C
27) history z-score = 0.67; physics z-score = 4.05; The student performed better on the physics test.
28) B
29) B
30) A
31) D
32) D
33) A
34) B
35) C
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