Chapter 6 Review
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Apr 3, 2024
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Math 1342 Statistics
Review Chapter 6
Name : ________________________________________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
Which of the following characteristics does not apply to a theoretical normal
distribution?
1)
A)
It is never negative.
B)
It is bell-shaped.
C)
It is bimodal.
D)
The mean, median, and mode are equal.
2)
In applied statistics, it is the area under the normal distribution curve which is most
important, not the value of single points on the curve.
2)
A)
False
B)
True
3)
If a normal distribution has a mean of 20 and a standard deviation of 10, then
3)
A)
the median is 30 and the mode is 10.
B)
the median is 10 and the mode is 30.
C)
the median is 20 and the mode is 20.
D)
the median is 20 and the mode is 30.
4)
The area under a normal distribution curve is always positive even if the z
value is
negative.
4)
A)
True
B)
False
5)
The figure below is an example of a negatively skewed distribution.
5)
A)
False
B)
True
6)
When the data values are evenly distributed about the mean, the distribution is said to be
.
6)
A)
symmetrical
B)
normal
C)
bimodal
D)
uniform
1
7)
Stating that the area under the standard normal distribution curve between z
= 0 and
z
= 1.00 is 0.3413, is the same as stating that the of randomly selecting a
standard normally distributed variable z with a value between 0 and 1.00 is 0.3413.
7)
A)
probability
B)
range
C)
score
D)
error
8)
Find the area under the standard normal distribution curve between z
= 0 and z
= 2.16.
8)
A)
0.9846
B)
0.4846
C)
0.3708
D)
2.1600
9)
Find the area under the standard normal distribution curve between z
= 0 and z
= -2.16.
9)
A)
0.9846
B)
0.3708
C)
–2.1600
D)
0.4846
10)
Find the area under the standard normal curve to the left of z
= 1.9.
10)
A)
0.4857
B)
0.4713
C)
0.9713
D)
0.0287
11)
Find the area under the standard normal curve to the right of z
= 2.7.
11)
A)
0.0035
B)
0.4965
C)
0.9965
D)
0.0018
12)
The probability P
(0 < z
< 0.97) is 0.3340.
12)
A)
True
B)
False
2
13)
What is the area under the standard normal distribution curve between z
= 1.50 and
z
= 2.50?
13)
A)
1.00
B)
0.0606
C)
0.0802
D)
0.0764
14)
Find the z
value that corresponds to the given area.
14)
A)
0.07
B)
–1.46
C)
1.23
D)
1.46
15)
Find the z
-score for which the area to the right is 0.52.
15)
A)
0.13
B)
-0.26
C)
-0.12
D)
-0.05
16)
Find the z
value that corresponds to the given area.
16)
A)
-1.52
B)
-0.17
C)
0.17
D)
1.52
17)
If a normally distributed group of test scores have a mean of 70 and a standard deviation
of 12, find the percentage of scores that will fall below 50.
17)
A)
45.25%
B)
6.75%
C)
4.75%
D)
35.54%
3
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18)
A normal population has a mean ȝ
= 31 and standard deviation ı
= 8. What proportion of
the population is less than 29?
18)
A)
0.7517
B)
0.4013
C)
0.5987
D)
1.0000
19)
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters
(mL) and standard deviation 7 mL. The fill volumes are normally distributed. What is
the probability that a bottle has a volume greater than 992 mL?
19)
A)
0.8413
B)
0.8810
C)
1.0000
D)
0.9987
20)
The average length of crocodiles in a swamp is 12.5 feet. If the lengths are normally
distributed with a standard deviation of 2.1 feet, find the probability that a crocodile is
more than 12 feet long.
20)
A)
0.09
B)
0.91
C)
0.41
D)
0.59
21)
The average height of flowering cherry trees in a certain nursery is 9.5 feet. If the
heights are normally distributed with a standard deviation of 1.3 feet, find the probability
that a tree is less than 11.5 feet tall.
21)
A)
0.82
B)
0.97
C)
0.88
D)
0.94
22)
X
is a normally distributed random variable with a standard deviation of 4.00. Find the
mean of X
when 64.8% of the area lies to the left of 8.52. (Note: the diagram is not
necessarily to scale.)
22)
A)
4.8
B)
8.4
C)
6.7
D)
7.0
23)
A(n) is a distribution of means obtained from samples
of a specific size taken from a population.
23)
A)
sampling error
B)
normal distribution
C)
mean distribution
D)
sampling distribution of sample means
4
24)
The difference between a sample mean and the population mean may be referred to as
.
24)
A)
the variance
B)
sampling error
C)
skewness
D)
the standard deviation
25)
The standard deviation of sample means will be larger than the standard deviation of the
population.
25)
A)
True
B)
False
26)
As the sample size n
increases, the shape of the distribution of the sample means taken
with replacement from a population with mean ȝ
and standard deviation ı
, will approach
a normal distribution. This distribution will have a mean of ȝ
and a standard deviation of
ı
n
. This is a statement of the .
26)
A)
law of large numbers
B)
sample error of the mean
C)
rule of the mean
D)
central limit theorem
27)
A sample of size 95 will be drawn from a population with mean 25 and standard
deviation 13. Find the probability that x
will be between 22 and 27.
27)
A)
0.0668
B)
0.9210
C)
0.9080
D)
0.0122
28)
A sample of size 39 will be drawn from a population with mean 23 and standard
deviation 10. Find the probability that x
will be greater than 25.
28)
A)
0.8944
B)
0.1292
C)
0.1056
D)
0.0951
29)
The mean annual income for people in a certain city (in thousands of dollars) is 38, with
a standard deviation of 33. A pollster draws a sample of 39 people to interview. What is
the probability that the sample mean income is between 36 and
40 (thousands of dollars)?
29)
A)
0.6480
B)
0.3520
C)
0.2961
D)
0.7039
30)
The average age of doctors in a certain hospital is 47.0 years old. Suppose the
distribution of ages is normal and has a standard deviation of 8.0 years. If 9 doctors are
chosen at random for a committee, find the probability that the average age of those
doctors is less than 48.9 years. Assume that the variable is normally distributed.
30)
A)
75.8%
B)
25.8%
C)
24.2%
D)
59.8%
31)
Use the normal approximation to the binomial to find that probability for the specific
value of X
.
n
= 30, p
= 0.7, X
= 20
31)
A)
0.47
B)
0.7
C)
0.15
D)
0.67
5
32)
Use the normal approximation to find the indicated probability. The sample size is n
, the
population proportion of successes is p
, and X
is the number of successes in the sample.
n
= 84, p
= 0.4: P
(
X
> 26)
32)
A)
0.9429
B)
0.0643
C)
0.9357
D)
0.9484
33)
Use the normal approximation to find the indicated probability. The sample size is n
, the
population proportion of successes is p
, and X
is the number of successes in the sample.
n
= 80, p
= 0.59: P
(
X
57)
33)
A)
0.9896
B)
0.9904
C)
0.9925
D)
0.0096
34)
Use the normal approximation to find the indicated probability. The sample size is n
, the
population proportion of successes is p
, and X
is the number of successes in the sample.
n
= 105, p
= 0.72: P
(71 < X
< 82)
34)
A)
0.7130
B)
0.1867
C)
0.1003
D)
0.8997
35)
Use the normal approximation to find the indicated probability. The sample size is n
, the
population proportion of successes is p
, and X
is the number of successes in the sample.
n
= 96, p
= 0.36: P
(29
X
43)
35)
A)
0.0985
B)
0.9713
C)
0.0287
D)
0.8728
6
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Answer Key
Testname: CHAPTER 6 REVIEW
1)
C
2)
B
3)
C
4)
A
5)
A
6)
A
7)
A
8)
B
9)
D
10)
C
11)
A
12)
A
13)
B
14)
D
15)
D
16)
A
17)
C
18)
B
19)
A
20)
D
21)
D
22)
D
23)
D
24)
B
25)
B
26)
D
27)
B
28)
C
29)
C
30)
A
31)
C
32)
A
33)
B
34)
A
35)
D
7