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Name:_________________________
Date:_____________
Chapter 6 Test : Normal Probability Distributions
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Applied and Computational Questions
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The random variable z is the standard normal score. Find z as shown in the diagram
below given that the area of the shaded region is 0.4927.
z
ANSWER:
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0
When using the notation z ( ) , the number  in parenthesis is the measure of the area to
the right of the z-score. Use this fact to find the z value corresponding to
a. z(0.08)
ANSWER: _________________
b. z(0.78)
ANSWER: _________________
c. z(0.8980)
ANSWER: _________________
d. z(0.50)
ANSWER: _________________
Find the probability that a piece of data picked at random from a normal
population would have a standard score, z, that lies:
a. Between z = 0 to z = -1.89
ANSWER: _________________
b. To the left of 1.01
ANSWER: _________________
c. To the right of -2.35
ANSWER: _________________
d. Between z = 0.61 to z = 2.93
ANSWER: _________________
Find the probabilities:
a. P(-2.10<z<2.35)
ANSWER: _________________
b. P(z>0.13)
ANSWER: _________________
c. P(z<3.67)
ANSWER: _________________
d. P(1.28<z<2.86)
ANSWER: _________________
Suppose daycare costs are normally distributed with a mean equal to $7000, and a
standard deviation equal to $1500.
a. What percentage of daycare centers cost between $4000 and $8000? ______
b. What percentage of daycare centers cost more than $9000?
____________
c. What percentage of daycare centers cost less than $5000? ________________
Find the z-score for the standard normal distribution such that:
a. 80% of the distribution is below(to the left of) this value
____________
b. The area to the right of this value is .15 ______________________________
Find the normal approximation for the binomial probability P(x≥9), where n = 12
p = 0.75.Compare this to the value you obtain using the binomial probability function
P(x≥9).
Normal approximation of probability:
________________________
Binomial probability:
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X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the
following probabilities:
a. P(X < 70.0)
__________________
b. P(72.5 <X < 80.0)
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c. P(X > 82.5)
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Use the standard normal table to find the following values of z:
a. z(0.9940)
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b. z(0.2054)
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c. z(0.3315)
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d. z(0.7881)
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Name:_________________________
Date:_____________
Chapter 6 Test : Normal Probability Distributions
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Consider a binomial distribution with 15 identical trials, and probability of success of
0.5.
a. Use the binomial tables to find P(3 < x  7).
__________________
b. Use the normal approximation to find P(3 < x  7).
__________________
Find the probability that a piece of data picked at random from a normally distributed
population will have a standard score that is
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b.
c.
d.
e.
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less than 2.00
greater than –1.40
less than –1.75
less than 1.25
greater than –1.58
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Given that x is a normally distributed random variable with a mean of 70 and a standard
deviation of 10, find the following probabilities.
a. P(x > 70)
__________________
b. P(70 < x < 82)
__________________
c. P(67 < x < 93)
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d. P(75 < x < 92)
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e. P(48 < x < 88)
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f. P(x < 48)
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The SAT scores attained by the students in Iowa City are approximately normally
distributed with a mean of 500 and a standard deviation of 80.
a. Find the percentage of students who score between 550 and 650.
b. Find the percentage of students who score less than 700. __________________
c. Find the 3rd quartile
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d. Find the 15 percentile, P15
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th
e. Find the 95 percentile, P95
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