6.1-6.2 Study Guide

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6.1-6.2 Quiz
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
1) X is a normally distributed random variable with a mean of 11.00. If the probability
that X is less than 11.88 is 0.67 (as shown below), then what is the standard deviation of
X? (Note: the diagram is not necessarily to scale.)
A) 4.00
B) 2.40
C) 1.00
1)
D) 2.00
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
2) What is the z value such that 50% of the total area under the standard normal
distribution curved lies to the right of it?
2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
3) The area under the normal distribution curve that lies within three standard deviations
of the mean is approximately 95%.
A) True
B) False
3)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
4) Find the z value to the right of the mean so that 62.93% of the area under the
distribution curve lies to the left of it.
1
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
5) Find the z-scores that bound the middle 74% of the area under the standard normal
curve.
A) -0.99, 0.99
B) -1.24, 1.24
C) -1.07, 1.07
D) -1.13, 1.13
5)
6) X is a normally distributed random variable with a mean of 4.0. Find the standard
deviation of the distribution if 59.10% of the data lies to the right of 3.54. (Note: the
diagram is not necessarily to scale.)
6)
A) 1.3
B) 2.0
C) 1.0
D) 0.5
7) One normal curve has a mean of 24 and a standard deviation of 3. A second normal
curve has a mean of 3 and a standard deviation of 24. The curve that is more dispersed,
or spread out, is
A) neither; by definition,a normal curve shows no spread.
B) both; they are equally spread out.
C) the second normal curve.
D) the first normal curve.
7)
8) Find the z value that corresponds to the given area.
8)
A) –0.22
B) 1.33
C) –0.51
2
D) 0.41
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
9) 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
9)
randomly selecting a standard normally distributed variable z with a value
between 0 and 1.00 is 0.3413.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
10) A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters
(mL) and standard deviation 7 mL. The fill volumes are normally distributed. What
proportion of bottles have volumes greater than 999 mL?
A) 0.4443
B) 0.8051
C) 1.0000
D) 0.6293
10)
11) The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the
wages are normally distributed with a standard deviation of $0.45. If a worker at this
fast food restaurant is selected at random, what is the probability that the worker earns
more than $6.75?
A) 5.2%
B) 28.8%
C) 42.1%
D) 27.6%
11)
12) Which choice is another term that can be used to describe a normal distribution:
A) bell curve
B) independent variable
C) negatively or positively skewed
D) discrete distribution
12)
13) The number of standard deviations a particular X value is from the mean is commonly
referred to as
.
13)
A)
C) 2
B) P(X)
D) z
14) A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters
(mL) and standard deviation 5 mL. The fill volumes are normally distributed. What
proportion of bottles have volumes between 992 mL and 998 mL?
A) 0.4207
B) 0.6452
C) 0.3399
D) 0.0808
14)
15) For a normal distribution curve with a mean of 15 and a standard deviation of 5, which
range of the variable defines an area under the curve corresponding to a probability of
approximately 68%?
A) from 12.5 to 17.5
B) from 10 to 20
C) from 5 to 25
D) from 15 to 25
15)
3
16) A normal population has a mean = 40 and standard deviation
of the population is between 24 and 32?
A) 0.8408
B) 0.1592
C) 0.0735
= 11. What proportion
16)
D) 0.2327
17) Identify the type of distribution pattern that occurs when the majority of the data values
fall to the left of the mean?
A) negatively skewed
B) left skewed
C) positively skewed
D) symmetrical
17)
18) The area under a normal distribution curve is always positive even if the z value is
negative.
A) True
B) False
18)
19) Find the probability P(z < 0.37) using the standard normal distribution.
A) 0.6300
B) 0.1443
C) 0.3557
D) 0.6443
19)
20) On an easy test, the mean score was 96 out of a possible 100 points. The distribution of
the test scores is likely to be
A) symmetric.
B) negatively skewed.
C) diagonally skewed.
D) positively skewed.
20)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
21) Mrs. Smith's reading class can read an average of 175 words per minute with a
standard deviation of 20 words per minute. The top 3% of the class is to receive
a special award. What is the minimum number of words per minute a student
would need to read in order to get the award? Assume the data is normally
distributed.
21)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
22) To find the area under the standard normal distribution curve between two z values, one
first finds the difference between the two z values, then locates the value corresponding
to that difference in the Standard Normal Distribution table.
A) True
B) False
22)
23) The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas
mileages are normally distributed with a standard deviation of 0.75 miles per gallon,
find the probability that a car has a gas mileage of between 29.8 and 30.2 miles per
gallon.
A) 0.107
B) 0.287
C) 0.273
D) 0.213
23)
4
24) The figure below is an example of a negatively skewed distribution.
A) True
24)
B) False
25) Find the z-score for which the area to the right is 0.27.
A) 0.82
B) 0.52
C) 0.34
25)
D) 0.61
26) X is a normally distributed random variable with a standard deviation of 2.00. Find the
mean of X if 12.71% of the area under the distribution curve lies to the right of 10.28.
(Note: the diagram is not necessarily to scale.)
A) 7.5
B) 8.0
C) 9.6
26)
D) 8.7
27) Find the probability P(z > -0.54) using the standard normal distribution.
A) 0.7946
B) 0.2054
C) 0.2946
D) 0.7054
27)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
28) When the data values are evenly distributed about the mean, the distribution is
said to be
.
28)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
29) 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.
A) 6.75%
B) 4.75%
C) 35.54%
D) 45.25%
5
29)
30) When the majority of the data values fall to the right of the mean, the distribution is said
to be left-skewed.
A) False
B) True
30)
31) X is a normally distributed random variable with a mean of 10 and a standard deviation
of 4.0. Find the value of X for which 70.54% of the area under the distribution curve
lies to the right of it. (Note: the diagram is not necessarily to scale.)
31)
A) 7.84
B) 8.92
C) 11.89
D) 8.56
32) Find the area under the standard normal distribution curve between z = –2.05 and z =
2.05.
A) 0.9876
B) 0.9596
C) 0.4798
D) 0.4938
33) Find the z value that corresponds to the given area.
A) 0.07
B) 1.23
C) 1.46
6
32)
33)
D) –1.46
34) In a standard normal distribution, what z value corresponds to 17% of the data between
the mean and the z value?
A) 0.44
B) 1.25
C) 2.10
D) 0.52
34)
35) Find the z value that corresponds to the given area.
35)
A) –0.79
B) 0.57
C) 0.27
36) Find the area under the standard normal curve to the left of z = 1.5.
A) 0.4332
B) 0.9332
C) 0.4666
D) 0.44
36)
D) 0.0668
37) Find the probability P(0.16 < z < 1.23) using the standard normal distribution.
A) 0.8271
B) 0.3600
C) 0.6729
D) 0.3271
37)
38) The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a
mean 8.9 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a
money-back guarantee that her 6-week poults will weigh at least a certain amount. What
weight should she guarantee so that she will have to give her customer's money back
only 1% of the time?
A) 4.92 lb
B) 3.58 lb
C) 4.02 lb
D) 4.47 lb
38)
39) 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.
A) True
B) False
39)
40) Which of the following properties distinguishes the standard normal distribution from
other normal distributions?
A) The mean is 0 and the standard deviation is 1.
B) The total area under the curve is equal to 1.00.
C) The mean is located at the center of the distribution.
D) The curve is continuous.
40)
7
41) If a normal distribution has a mean of 35 and a standard deviation of 10, then
A) the median is 45 and the mode is 25.
B) the median is 35 and the mode is 45.
C) the median is 25 and the mode is 45.
D) the median is 35 and the mode is 35.
41)
42) Find the probability P(0 < z < 1.67), using the standard normal distribution.
A) 45.25%
B) 42.07%
C) 45.54%
D) 35.54%
42)
43) X is a normally distributed random variable with a standard deviation of 3.50. Find the
mean of X when 64.8% of the area lies to the left of 5.33. (Note: the diagram is not
necessarily to scale.)
43)
A) 3.7
B) 5.2
C) 2.1
D) 4.0
44) The normal distribution curve can be used as a probability distribution curve for
normally distributed variables.
A) True
B) False
8
44)
Answer Key
Testname: 6.1-6.2 QUIZ
1) D
2) zero
3) B
4) 0.33
5) D
6) B
7) C
8) A
9) probability
10) A
11) B
12) A
13) D
14) C
15) B
16) B
17) C
18) A
19) D
20) B
21) 213
22) B
23) D
24) B
25) D
26) B
27) D
28) symmetrical
29) B
30) B
31) A
32) B
33) C
34) A
35) B
36) B
37) D
38) D
39) A
40) A
41) D
42) A
9
Answer Key
Testname: 6.1-6.2 QUIZ
43) D
44) A
10
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