Chapter 6 Discrete Probability Distributions
Ch 6.1 Discrete Random Variables
Objective A: Discrete Probability Distribution
A1. Distinguish between Discrete and Continuous Random Variables
Example 1: Determine whether the random variable is discrete or continuous.State the possible values
of the random variable.
(a) The number of fish caught during the fishing tournament.
(b) The distance of a baseball travels in the air after being hit.
A2. Discrete Probability Distributions
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Example 1: Determine whether the distribution is a discrete probability distribution. If not, state why.
Example 2: (a) Determine the required value of the missing probability to make the distribution
a discrete probability distribution.
(b) Draw a probability histogram.
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Objective B: The Mean and Standard Deviation of a Discrete Random Variable
Example 1: Find the mean, variance, and standard deviation of the discrete random variable x .
(a) Mean x  [ x  P( x)]
P( x)
0.073
0.117
0.258
0.322
0.230
x
0
1
2
3
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(b) Variance
0
P( x)
0.073
1
0.117
2
0.258
3
4
0.322
0.230
x
--->
x  P( x)
Use the definition formula
 x 2  [( x  x )2  P( x)]
Formula (2a) in the textbook
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Chapter 6.2 The Binomial Probability Distribution
Objective A : Criteria for a Binomial Probability Experiment
The binomial probability distribution is a discrete probability distribution that obtained from a
binomial experiment.
Example 1: Determine which of the following probability experiments represents a binomial
experiment.If the probability experiment is not a binomial experiment, state why.
(a) A random sample of 30 cars in a used car lot is obtained, and their mileages
recorded.
(b) A poll of 1,200 registered voters is conducted in which the repondents are asked
whether they believe Congress should reform Social Security.
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Objective B : Binomial Formula
Let the random variable x be the number of successes in n trials of a binomial experiment.
Example 1: A binomial probability experiment is conducted with the given parameters.
Compute theprobability of x successes in the n independent trials of the
experiment.
n  15, p  0.85, x  12 (Round to four decimal places as needed)
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Example 2: (a) Use StatCrunch to compute a Binomial table of n  4 and p  0.65 .
First state the possible values of the random variable x then select
Stat  Calculators  Binomial and input n  4 and p  0.65 then each x value.
x
P( x)
(b) Use the Binomial table from part (a), find P ( x  2) .
(c) Use the Binomial table from part (a), find P(0  x  3) .
Objective C : Binomial Table by StatCunch
Example 1: Use StatCrunch with Binomial Distribution to find P ( x  6) with n  12 and p  0.4 .
Example 2: According to the American Lung Association, 90% of adult smokers started smoking
before turning 21 years old. Ten smokers 21 years old or older are randomly selected,
and the number of smokers who started smoking before 21 is recorded.
(a) Explain why this is a binomial experiment.
(b) Use StatCrunch to find the probability that exactly 8 of them started smoking
before 21 years of age.
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(c) Use StatCrunch to find the probability that at least 8 of them started smoking
before 21 years of age.
(d) Use StatCrunch to find the probability that between 7 and 9 of them, inclusive,
started smoking before 21 years of age.
Objective D : Mean and Standard Deviation of a Binomial Random Variable
Example 1: A binomial probability experiment is conducted with the given parameters.
Compute the mean and standard deviation of the random variable x .
n  9 p  0.8
Example 2: According to the 2005 American Community Survey, 43% of women aged 18 to 24
were enrolled in college in 2005.
(a) For 500 randomly selected women ages 18 to 24 in 2005, compute the mean
and standarddeviation of the random variable x , the number of women who
were enrolled in college.
(b) Interpret the mean.
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What role do p and n play in the shape of a binomial distribution? Study the textbook pg. 318-319.
In Other Words
Provided that np(1  p)  10, the interval   2 to   2 represent the “usual” observations. Observations
outside this interval may be considered unusual.
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