Answer to Question #138174 in Statistics and Probability for James

Question

A bottle maker believes that 12% of his bottles are defective.

If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 412 bottles would be greater than 11%? Round your answer to four decimal places.

Answer 1

solution

Population proportion, $p=0.12$

Sample proportion, $\hat p=0.11$

$$Z = \frac{\hat p -p}{\sqrt{\frac{p(1-p)}{n}}}$$

$$\frac{0.11 -0.12}{\sqrt{\frac{0.12(1-0.12)}{412}}}=-0.6246$$

When the Z score is -0.6246, the probability that $Z>-0.6246$ is $0.73388$

answer:

The probability that the proportion is greater than 0.11 is 0.7339