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. If a manufacturer randomly selects 21 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 $\frac { 1 } { 7 }$.
B) We are $95 \%$ confident that $p$ does not exceed $\frac { 1 } { 7 }$.
C) We are $95 \%$ confident that $p$ lies between $\frac { 1 } { 21 }$ and $\frac { 1 } { 7 }$.
D) The value of $p$ cannot be greater than $\frac { 1 } { 7 }$.

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. If a manufacturer randomly selects 21 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 $\frac { 1 } { 7 }$.
B) We are $95 \%$ confident that $p$ does not exceed $\frac { 1 } { 7 }$.
C) We are $95 \%$ confident that $p$ lies between $\frac { 1 } { 21 }$ and $\frac { 1 } { 7 }$.
D) The value of $p$ cannot be greater than $\frac { 1 } { 7 }$.

Quizplus · Accepted Answer

The Rule of Three states that if n trials of a binomial experiment result in no successes, we can be 95% confident that the true population proportion (p) of successes is less than or equal to 3/n. Given n = 21, the upper bound for p is 3/21 = 1/7. Therefore, we are 95% confident that the proportion of defective computers does not exceed 1/7.

Solve the Problem 95%95 \%95% Confident That ppp Is Greater Than 17\frac { 1 } { 7 }71​

Solve the Problem $95 \%$ Confident That $p$ Is Greater Than $\frac { 1 } { 7 }$