Concept explainers
a.
Compute the
a.
Answer to Problem 17P
The probability that at least 6 wolves were males is 0.740.
The probability that at least 6 wolves were females is 0.473.
The probability that less than 4 wolves were females is 0.135.
Explanation of Solution
Calculation:
A trial determines the sex of a wolf with two possible outcomes, success or failure. Consider success as male and failure as female.
The total number of wolves (or trials) is
The probability of male wolves (or success) is
The probability of female wolves (or failure) is
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.
Probability that at least 6 wolves were males:
The probability that at least 6 wolves were males is calculated as given below:
Therefore, the probability that at least 6 wolves were males is 0.740.
Probability that at least 6 wolves were females:
Six or more females are same as less than or equal to males.
The probability that at least 6 wolves were females is calculated as given below:
Therefore, the probability that at least 6 wolves were females is 0.473.
Probability that less than 4 wolves were females:
Less than 4 females are the same as more than 8 males.
The probability that less than 4 wolves were females is calculated as given below:
Therefore, the probability that less than 4 wolves were females is 0.135.
b.
Compute the probability that at least 6 wolves were males, at least 6 wolves were females, and less than 4 wolves were females from 1918 to present.
b.
Answer to Problem 17P
The probability that at least 6 wolves were males is 0.961.
The probability that at least 6 wolves were females is 0.117.
The probability that less than 4 wolves were females is 0.493.
Explanation of Solution
Calculation:
A trial determines the sex of a wolf with two possible outcomes success or failure. Consider success as male and failure as female.
The total number of wolves (or trials) is
The probability of male wolves (or success) is
The probability of female wolves (or failure) is
Probability that at least 6 wolves were males:
The probability that at least 6 wolves were males is calculated as given below:
Therefore, the probability that at least 6 wolves were males is 0.961.
Probability that at least 6 wolves were females:
Six or more females are the same as less than or equal to males.
The probability that at least 6 wolves were females is calculated as given below:
Therefore, the probability that at least 6 wolves were females is 0.117.
Probability that less than 4 wolves were females:
Less than 4 females are the same as more than 8 males.
The probability that less than 4 wolves were females is calculated as given below:
Therefore, the probability that less than 4 wolves were females is 0.493.
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Chapter 5 Solutions
Understandable Statistics: Concepts and Methods
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