(a)
To find:
The specified probability for the given scenario.
Answer to Problem 25E
Solution:
Value of the required probability is 0.9952.
Explanation of Solution
Given information:
Ronnie owns a fireworks stand and knows that in the fireworks business, 1 out of every 13 fireworks is a dud. Suppose that Juanita buys 10 firecrackers at Ronnie’s stand.
Formula used:
For a binomial random variable
The formula to calculate
Here,
The formula to calculate
Calculation:
Consider the event “duds” as a success.
Probability of winning is 1 out of 13.
Probability of success is
Number of trial is 10.
Compute the probability for no more than 3 successes.
Substitute 3 for
Substitute 10 for
Substitute 10 for
Substitute 10 for
Substitute 10 for
Add the values of
Conclusion:
Thus, the probability that no more than 3 are duds is 0.9952.
(b)
To find:
The specified probability for the given scenario.
Answer to Problem 25E
Solution:
Value of the required probability is 0.45.
Explanation of Solution
Given information:
Ronnie owns a fireworks stand and knows that in the fireworks business, 1 out of every 13 fireworks is a dud. Suppose that Juanita buys 10 firecrackers at Ronnie’s stand.
Formula used:
For a binomial random variable
The formula to calculate
Calculation:
Consider the event “duds” as a success.
Probability of winning is 1 out of 13.
Probability of success is
Number of trial is 10.
Compute the probability for no success.
Substitute 10 for
Conclusion:
Thus, the probability of no duds is 0.45.
(c)
To find:
The specified probability for the given scenario.
(c)
Answer to Problem 25E
Solution:
Value of the required probability is 0.00003.
Explanation of Solution
Given information:
Ronnie owns a fireworks stand and knows that in the fireworks business, 1 out of every 13 fireworks is a dud. Suppose that Juanita buys 10 firecrackers at Ronnie’s stand.
Formula used:
For a binomial random variable
The formula to calculate
Here,
The formula to calculate
Calculation:
Consider the event “duds” as a success.
Probability of winning is 1 out of 13.
Probability of success is
Number of trial is 10.
Consider number of more than half of the crackers as a number of success.
Compute the probability for more than 5 successes.
Substitute 5 for
Substitute 10 for
Substitute 10 for
Substitute 10 for
Substitute 10 for
Substitute 10 for
Add all the values of
Conclusion:
Thus, the probability of more than half duds is 0.00003.
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Chapter 5 Solutions
Beginning Statistics
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