Ch. 7
The Normal Probability Distribution
7.1
Properties of the Normal Distribution
1
Understand the Uniform Probability Distribution
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 70°F
to 91°F. What is the probability that a randomly selected August day has a high temperature that exceeded
75°F?
A) 0.7619
B) 0.2381
C) 0.4658
D) 0.0476
2) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 80°F
to 110°F. Find the high temperature which 90% of the August days exceed.
A) 83°F
B) 107°F
C) 90°F
D) 110°F
3) The diameter of ball bearings produced in a manufacturing process can be explained using a uniform
distribution over the interval 4.5 to 6.5 millimeters. What is the probability that a randomly selected ball
bearing has a diameter greater than 5.2 millimeters?
4) Suppose x is a uniform random variable with c
=
10 and d
=
90. Find the probability that a randomly selected
observation exceeds 26.
5) Suppose x is a uniform random variable with c
=
10 and d
=
70. Find the probability that a randomly selected
observation is between 13 and 65.
6) A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is
learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the
interval 9.5 to 12.5 gallons per minute. Find the probability that between 10.0 gallons and 11.0 gallons are
pumped during a randomly selected minute.
A) 0.33
B) 0.67
C) 0
D) 1
7) Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes
ranging from 30 to 80. What is the probability that this experiment results in an outcome less than 40?
8) A random number generator is set top generate integer random numbers between 1 and 10 inclusive following
a uniform distribution. What is the probability of the random number generator generating a 7?
9) True or False: In a uniform probability distribution, any random variable is just as likely as any other random
variable to occur, provided the random variables belong to the distribution.
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2
Graph a Normal Curve
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) You are performing a study about the weight of preschoolers. A previous study found the weights to be
normally distributed with a mean of 30 and a standard deviation of 4. You randomly sample 30 preschool
children and find their weights to be as follows.
25
25
26
26.5
27
27
27.5
28
28
28.5
29
29
30
30
30.5
31
31
32
32.5
32.5
33
33
34
34.5
35
35
37
37
38
38
a) Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed?
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 Spring '10
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 Normal Distribution, Standard Deviation, Exponentiation, σ, MULTIPLE CHOICE. Choose

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