a.
Calculate the
a.
Answer to Problem 26P
The probability that all six professors are extroverts is 0.008.
Explanation of Solution
Calculation:
Let r follows a binomial distribution that represents the number of professors who are extroverts with success described as “extroverts” and failure described as “not extroverts”.
Total number of professors (or trials)
Probability of extrovert professors
Probability of non-extrovert professors (or failure) is calculated as given below:
Binomial probability:
The probability of r successes out of n trials is given below:
Here, n is the number of trials, r is the number of successes, p is the probability of success, and q is the probability of failure.
The probability that all six professors are extroverts is calculated as given below:
Thus, the probability that all six professors are extroverts is 0.008.
b.
Calculate the probability that none of the professors are extroverts.
b.
Answer to Problem 26P
The probability that none of the professors are extroverts is 0.028.
Explanation of Solution
Calculation:
The probability that none of the professors are extroverts is calculated as given below:
Thus, the probability that none of the professors are extroverts is 0.028.
b.
Calculate the probability that none of the professors are extroverts.
b.
Answer to Problem 26P
The probability that none of the professors are extroverts is 0.028.
Explanation of Solution
Calculation:
The probability that none of the professors are extroverts is calculated as given below:
Thus, the probability that none of the professors are extroverts is 0.028.
c.
Calculate the probability that at least two of the professors are extroverts.
c.
Answer to Problem 26P
The probability that at least two of the professors are extroverts is 0.836.
Explanation of Solution
Calculation:
The probability that at least two of the professors are extroverts is calculated as given below:
Thus, the probability that at least two of the professors are extroverts is 0.836.
d.
Calculate the expected number of extroverts.
Calculate the standard deviation.
d.
Answer to Problem 26P
The expected number of extroverts is 2.7.
The standard deviation is 1.219.
Explanation of Solution
Calculation:
The expected number of extroverts is calculated as given below:
Thus, the expected number of extroverts is 2.7.
The standard deviation is calculated as given below:
Thus, the standard deviation is 1.219.
e.
Calculate the number of professors to be interviewed to be 90% certain that at least 3 professors will be extroverts.
e.
Answer to Problem 26P
The number of professors to be interviewed to be 90% certain that at least 3 professors will be extroverts is 10.
Explanation of Solution
Calculation:
Compute n such that
The probability that at least 3 professors will be extroverts is calculated as given below:
Using Table 3, Appendix II: Binomial distribution table, the probability values for
Therefore, for
Thus, 10 professors have to be interviewed to be 90% certain that at least 3 professors will be extroverts.
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Chapter 5 Solutions
Understandable Statistics: Concepts and Methods
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning