1. A continuous random variable is a random variable that can:
A) assume only a countable set of values
B) assume any value in one or more intervals
C) have no random sample
D) assume no continuous random frequency
2. The relative frequency density for a class is obtained by dividing the:
A) frequency of that class by the class width
B) relative frequency of that class by the total frequency
C) relative frequency of that class by the class width
D) frequency of that class by the relative frequency
3. For a continuous random variable x, the probability that x assumes a value in an interval
is:
A) in the range zero to 1 B) greater than 1 C) less than zero D) greater
than 2
4. For a continuous random variable x, the area under the probability distribution curve
between any two points is always:
A) greater than 1 B) less than zero C) equal to 1 D) in the range zero to 1
5. For a continuous random variable x, the total probability of all (mutually exclusive)
intervals within which x can assume a value is:
A) less than 1 B) greater than 1 C) equal to 1 D) between zero and 1
6. For a continuous random variable x, the total area under the probability distribution curve
of x is always:
A) less than 1 B) greater than 1 C) equal to 1 D) between zero and 1
7. The probability that a continuous random variable x assumes a single value is always:
A) less than 1 B) greater than zero C) equal to zero D) between zero and 1
Chapter 6
8. The normal probability distribution is applied to:
A) a discrete random variable C) any random variable
B) a continuous random variable D) a subjective random variable
9. Which of the following is not a characteristic of the normal distribution?
A) The total area under the curve is 1.0
B) The curve is symmetric about the mean
C) The value of the mean is always greater than the value of the standard deviation
D) The two tails of the curve extend indefinitely
10. The total area under a normal distribution curve to the left of the mean is always:
A) equal to 1 B) equal to zero C) equal to 0.5 D) greater than .5
11. The total area under a normal distribution curve to the right of the mean is always:
A) equal to 1 B) equal to zero C) equal to 0.5 D) greater than .5
12. The tails of a normal distribution curve:
A) meet the horizontal axis at z = 3.0
B) never meet or cross the horizontal axis
C) cross the horizontal axis at z = 4.0
D) are nonsymmetric
13. The parameters of the normal distribution are:
A)
and
B)
, , and x
C)
, , and z
D)
, , , and xz
14. For a normal distribution, the spread of the curve decreases and its height increases as:
A) the sample size decreases
B) the standard deviation decreases
C) the ratio of the mean and standard deviation increases
D) the mean increases
Chapter 6
15. For the standard normal distribution, the mean is:
A) 1 and the standard deviation is zero C) zero and the standard deviation is 1
B) 0.5 and the standard deviation is 0.5 D) 1 and the standard deviation is 1
16. For the standard normal distribution, the z value gives the distance between the mean and
a point in terms of the:
A) mean B) standard deviation C) variance D) center of the curve
17. For a normal distribution, the z value for an x value that is to the right of the mean is
always:
A) equal to zero B) negative C) greater than 1 D) positive
18. For a normal distribution, the z value for an x value that is to the left of the mean is
always:
A) equal to zero B) negative C) less than 1 D) positive
19. For a normal distribution, the z value for the mean is always:
A) equal to zero B) negative C) equal to 1 D) positive
20. For the standard normal distribution, the area between z = 0 and z = 1.70, rounded to four
decimal places, is:
21. For the standard normal distribution, the area between z = 0 and z = –1.38, rounded to
four decimal places, is:
22. For the standard normal distribution, the area to the right of z = 0.53, rounded to four
decimal places, is:
Chapter 6
23. For the standard normal distribution, the area to the right of z = –2.97, rounded to four
decimal places, is:
24. For the standard normal distribution, the area to the left of z = 1.23, rounded to four
decimal places, is:
25. For the standard normal distribution, the area to the left of z = –2.22, rounded to four
decimal places, is:
26. For the standard normal distribution, the area between z = 1.03 and z = 1.30, rounded to
four decimal places, is:
27. For the standard normal distribution, the area between z = –2.04 and z = 2.28, rounded to
four decimal places, is:
28. For the standard normal distribution, the area between z = –2.35 and z = –1.56, rounded
to four decimal places, is:
29. Let x have a normal distribution with a mean of 49.2 and a standard deviation of 4.90.
The z value for x = 56.05, rounded to two decimal places, is:
Chapter 6
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30. Let x have a normal distribution with a mean of 123.7 and a standard deviation of 6.01.
The z value for x = 133.67, rounded to two decimal places, is:
31. Let x have a normal distribution with a mean of 7.8 and a standard deviation of 3.58. The
z value for x = 10.27, rounded to two decimal places, is:
32. Let x have a normal distribution with a mean of –40.3 and a standard deviation of 11.51.
The z value for x = –26.58, rounded to two decimal places, is:
Use the following to answer questions 33-35:
The GMAT scores of all examinees who took that test this year produce a distribution that is
approximately normal with a mean of 420 and a standard deviation of 32.
33. The probability that the score of a randomly selected examinee is between 400 and 480,
rounded to four decimal places, is:
34. The probability that the score of a randomly selected examinee is less than 370, rounded
to four decimal places, is:
35. The probability that the score of a randomly selected examinee is more than 530, rounded
to four decimal places, is:
Use the following to answer questions 36-38:
The daily sales at a convenience store produce a distribution that is approximately normal with a
mean of 1220 and a standard deviation of 130.
Chapter 6
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36. The probability that the sales on a given day at this store are more than $1,405, rounded
to four decimal places, is:
37. The probability that the sales on a given day at this store are less than $1,305, rounded to
four decimal places, is:
38. The probability that the sales on a given day at this store are between $1,200 and $1,300,
rounded to four decimal places, is:
Use the following to answer questions 39-41:
The net weights of all boxes of Top Taste cookies produce a distribution that is approximately
normal with a mean of 31.74 and a standard deviation of 0.58.
39. The probability that the net weight of a randomly selected box of these cookies is more
than 32.6 ounces, rounded to four decimal places, is:
40. The probability that the net weight of a randomly selected box of these cookies is less
than 31.58 ounces, rounded to four decimal places, is:
41. The probability that the net weight of a randomly selected box of these cookies is
between 31.8 and 32.5 ounces, rounded to four decimal places, is:
Use the following to answer questions 42-44:
The heights of all female college basketball players produce a distribution that is approximately
normal with a mean of 67.55 and a standard deviation of 2.02.
Chapter 6
42. The probability that the height of a randomly selected female college basketball player is
more than 65.8 inches, rounded to four decimal places, is:
43. The probability that the height of a randomly selected female college basketball player is
less than 67.2 inches, rounded to four decimal places, is:
44. The probability that the height of a randomly selected female college basketball player is
between 63.9 and 69.2 inches, rounded to four decimal places, is:
45. The area under the standard normal curve from zero to z is 0.4906 and z is positive. The
value of z is:
46. The area under the standard normal curve from zero to z is 0.1772 and z is negative. The
value of z is:
47. The area under the standard normal curve to the right of z is 0.0089 and z is positive. The
value of z is:
48. The area under the standard normal curve to the left of z is 0.0401 and z is negative. The
value of z is:
Chapter 6
49. We can use the normal distribution to approximate the binomial distribution when:
A) the sample size is at least 30 C) np and nq are both more than 5
B) np and nq are both less than 5 D) nx is greater than 30
Use the following to answer questions 50-52:
We know that 57% of all adults are in favor of abolishing the sales tax and increasing the income
tax. Suppose we take a random sample of 420 adults and obtain their opinions on the issue.
50. The probability that exactly 250 will be in favor of abolishing the sales tax and increasing
the income tax is approximately:
51. The probability that 225 or fewer will be in favor of abolishing the sales tax and
increasing the income tax is approximately:
52. The probability that 250 to 265 will be in favor of abolishing the sales tax and increasing
Use the following to answer questions 53-55:
We know that football is the favorite sport to watch on television for 36% of adults in the United
States. Suppose we take a random sample of 522 adults and obtain their opinions on their
favorite sport to watch on television.
53. The probability that 180 to 215 will say that football is their favorite sport to watch on
television is approximately: (Round the answer to 4 decimal places.)
Chapter 6
54. The probability that 193 or more will say that football is their favorite sport to watch on
television is approximately: (Round the answer to 4 decimal places.)
55. The probability that 170 to 190 will say that football is their favorite sport to watch on
Use the following to answer questions 56-58:
In a recent Gallup poll, 52% of parents with children under 18 years of age gave themselves a
grade of B for the job they are doing bringing up their kids. Assume that this percentage is true
for the current population of all parents with children under 18 years of age. You take a random
sample of 1044 such parents and ask them to give themselves a grade for the job they are doing
bringing up their kids.
56. The probability that 560 or more will give themselves a grade of B is approximately:
(Round the answer to 4 decimal places.)
57. The probability that 550 or less will give themselves a grade of B is approximately:
(Round the answer to 4 decimal places.)
58. The probability that 520 to 555 will give themselves a grade of B is approximately:
(Round the answer to 4 decimal places.)
Chapter 6
59. The accountant at a department store is analyzing the credit card purchases of 100 of the
store’s cardholders over the past year. The following table lists the frequency distribution
of the continuous random variable x, annual credit card purchases.
Annual Credit Card
Purchases ($)
Frequency
0 to less than 200
14
200 to less than 400
18
400 to less than 600
15
600 to less than 800
25
800 to less than 1000
15
1000 to less than 1200
13
What is the relative frequency density of the 400 to less than 600 class? Round your
answer to 5 decimal places.
60. There are 250 players in a particular youth soccer league that has 11 teams. The league
statistician is tabulating the total goals scored over the past season by each player. She
assigns the random variable y to represent these totals, and then assigns the following
categories for y: 0 to less than 4, 4 to less than 8, 8 to less than 12, 12 to less than 16, 16
to less than 20, and 20 to less than 24. The relative frequency density for the 8 to less
than 12 class is 0.019. How many of the players scored between 8 and less than 12 goals?
61. You are given that the area under the standard normal curve to the left of z = –2.56 is
equal to 0.0052. What is P(–2.56< z < 2.56)?
62. We know that the length of time required for a student to complete a particular aptitude
test has a normal distribution with a mean of 41.5 minutes and a variance of 3.1 minutes.
What is the probability, rounded to four decimal places, that a given student will
complete the test in more than 36 minutes but less than 44 minutes?
Chapter 6
63. Suppose that the distribution for a random variable x is normal with mean 15 and
standard deviation
, and
( 0) 0.0773Px=
. Rounded to two decimal places, what is
?
64. As explained in the textbook, the normal distribution can be used as an approximation to
the binomial distribution when np > 5 and nq > 5. Let x be the number of times that heads
comes up in n flips of a coin for which the probability of a head is p = 0.152. What is the
lowest that n can be in order for us to use the normal approximation for the distribution of
x?
65. Suppose that the random variable x has a binomial distribution with n = 30 and p = 0.48.
You want to determine
( )
14 19PX
. Using the normal approximation, what is this
probability? (Round the answer to 4 decimal places.)
66. The ages of adults in a certain community follow a normal distribution with mean 38.5
and standard deviation 6.68. The random variable x represents the age of a randomly
selected adult from this community. Given that
( )
35 .17P x a =
, what is a to the
nearest year?
67. 95.8% of the parts coming off an assembly line are non-defective. Using the normal
approximation to the binomial distribution, what is the probability, rounded to four
decimal places, that of 504 parts, fewer than 480 are non-defective?
Chapter 6
68. A floor tiling contractor has just sent Tina out on a job without any indication of the size
of the job. She does know that, over the years, the number of tiles required for each job
has followed a normal distribution with a mean of 581 and a standard deviation of 210.
She can either take the large truck (which is very difficult and expensive to drive) or the
small truck to the job site. She is certain that the large truck can hold enough tiles to do
the job, but she would prefer to take the small truck if she can. The small truck can carry
up to 750 tiles. Because the job site is out of town, she can only make one trip. What is
the probability that the small truck will carry enough tiles to do the job?
69. Let x be a continuous random variable that follows a normal distribution with a mean of
218 and a standard deviation of 26.
Find the value of x so that the area under the normal curve to the left of x is
approximately 0.8770. Round your answer to two decimal places.
70. Let x be a continuous random variable that follows a normal distribution with a mean of
200 and a standard deviation of 51.
Find the value of x so that the area under the normal curve to the right of x is
approximately 0.2946. Round your answer to two decimal places.
71. Let x be a continuous random variable that follows a normal distribution with a mean of
226 and a standard deviation of 31.
Find the value of x so that the area under the normal curve between
and x is
approximately 0.4959 and the value of x is less than
. Round your answer to two
decimal places.
Chapter 6
72. Let x be a continuous random variable that follows a normal distribution with a mean of
207 and a standard deviation of 42.
Find the value of x so that the area under the normal curve between
and x is
approximately 0.4996 and the value of x is greater than
. Round your answer to two
decimal places.
73. According to the Empirical rule, what percent of the data should be between 136 and 260
for a population with mean of 198 and standard deviation of 62?
74. According to the Empirical rule, 68.26% of the data would fall between what two values
for a population with mean of 816 and standard deviation of 248?
75. For a normal curve, changing the mean from 35 to 46 will cause the curve to shift
A) to the left. B) to the right. C) up. D) down.