Concept explainers
FILE In a recent study, 90% of the homes in the United States were found to have large-screen TVs. In a sample of nine homes, what is the probability that:
- a. All nine have large-screen TVs?
- b. Less than five have large-screen TVs?
- c. More than five have large-screen TVs?
- d. At least seven homes have large-screen TVs?
a.
Compute the probability that all nine have large-screen TVs.
Answer to Problem 21E
The probability that all nine have large-screen TVs is 0.3874.
Explanation of Solution
The formula to find the binomial probability is as follows:
Here, n=9; π=0.90.
The probability that all nine have large-screen TVs is calculated as follows:
Therefore, the probability that all nine have large-screen TVs is 0.3874.
b.
Compute the probability that less than five have large-screen TVs.
Answer to Problem 21E
The probability that less than five have large-screen TVs is 0.0009.
Explanation of Solution
The probability that less than five have large-screen TVs is calculated as follows:
Therefore, the probability that less than five have large-screen TVs is 0.0009.
c.
Calculate the probability that more than five have large-screen TVs.
Answer to Problem 21E
The probability that more than five have large-screen TVs is 0.0083.
Explanation of Solution
The probability that more than five have large-screen TVs is calculated as follows:
Therefore, the probability that more than five have large-screen TVs is 0.0083.
d.
Calculate the probability that at least seven homes have large-screen TVs.
Answer to Problem 21E
The probability that at least seven homes have large-screen TVs is 0.947.
Explanation of Solution
The probability that at least seven homes have large-screen TVs is calculated as follows:
Therefore, the probability that at least seven homes have large-screen TVs is 0.947.
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