A recent poll indicated that about83​%of U.S. households had access to a​ high-speed Internet connection. a. Suppose 100 households were randomly selected from the United States. How many of the households would you expect to have access to a​ high-speed Internet​ connection?b. If20households are selected​ randomly, what is the probability that exactly12have​ high-speed access?c. If20households are selected​ randomly, what is the probability that12or fewer have​ high-speed access?a. Suppose 100 households were randomly selected from the United States. How many of the households would you expect to have access to a​ high-speed Internet​ connection?

Question
Asked Oct 23, 2019
A recent poll indicated that about
83​%
of U.S. households had access to a​ high-speed Internet connection.
 
a. Suppose 100 households were randomly selected from the United States. How many of the households would you expect to have access to a​ high-speed Internet​ connection?
b. If
20
households are selected​ randomly, what is the probability that exactly
12
have​ high-speed access?
c. If
20
households are selected​ randomly, what is the probability that
12
or fewer have​ high-speed access?
a. Suppose 100 households were randomly selected from the United States. How many of the households would you expect to have access to a​ high-speed Internet​ connection?
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Expert Answer

Step 1
  1. The expected number of households have access to a​ high-speed Internet​ connection is obtained below:

From the given information, the probability that U.S. households had access to a high-speed Internet connection is 83%. Let the random X be the number of U.S. households had access to a high-speed Internet connection.

The required value is,

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Step 2

b.The probability that exactly 12 have​ high-speed access is obtained below:

Using the EXCEL formula
=BINOM.DIST(12,20, 0. 83 ,FALSE)
P(X 12) 0.0094
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Using the EXCEL formula =BINOM.DIST(12,20, 0. 83 ,FALSE) P(X 12) 0.0094

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Step 3

c.The probability that 12 or fewer have​ high-speed access is ob...

Using the EXCEL formula
=BINOM.DIST (12,20,0. 83,TRUE)
P(X12) 0.0127
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Image Transcriptionclose

Using the EXCEL formula =BINOM.DIST (12,20,0. 83,TRUE) P(X12) 0.0127

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