Solve the problem.
-Suppose that n trials of a binomial experiment result in no successes. According to the "Rule of Three", we have 95% confidence that the true population proportion has an upper bound of 3/n $3 / n$ . If a manufacturer randomly Selects 25 computers for quality control and finds no defective computers, what statement can you make by Using the rule of three, about the proportion p, of all its computers which are defective?
A) We are $95 \%$ confident that $p$ is greater than $\frac { 3 } { 25 }$.
B) We are $95 \%$ confident that $p$ lies between $\frac { 1 } { 25 }$ and $\frac { 3 } { 25 }$.
C) We are $95 \%$ confident that p does not exceed $\frac { 3 } { 25 }$.
D) The value of p cannot be greater than $\frac { 3 } { 25 }$.

Question

Solve the problem.
-Suppose that n trials of a binomial experiment result in no successes. According to the "Rule of Three", we have 95% confidence that the true population proportion has an upper bound of 3/n $3 / n$ . If a manufacturer randomly Selects 25 computers for quality control and finds no defective computers, what statement can you make by Using the rule of three, about the proportion p, of all its computers which are defective? 
A) We are $95 \%$ confident that $p$ is greater than $\frac { 3 } { 25 }$.
B) We are $95 \%$ confident that $p$ lies between $\frac { 1 } { 25 }$ and $\frac { 3 } { 25 }$.
C) We are $95 \%$ confident that p does not exceed $\frac { 3 } { 25 }$.
D) The value of p cannot be greater than $\frac { 3 } { 25 }$.

Quizplus · Accepted Answer

The "Rule of Three" states that if there are no successes in a binomial experiment with n trials, then the upper bound of the population proportion with 95% confidence is 3/n. In this case, n = 25 (the sample size) and there were no defective computers, so the upper bound of the population proportion is 3/25. Therefore, we can say with 95% confidence that p (the proportion of all computers that are defective) does not exceed 3/25. This corresponds to choice C.

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