A toy company claims that 91% of its Good Guys dolls are defect-free. If a random sample of 180 Good Guys dolls is selected, what is the probability that more than 85% of the sample will be defect-free? Round your final answer to four decimal places.

Answer:
Given:
The population proportion $(p)=0.91$

The sample size $(n)=180$

Solution:
The probability that more than 85% of the sample will be defect free:
$P(\hat{p}>0.85)=P(\frac{\hat{p}–p}{\sqrt{\frac{p(1-p)}{n}}}>\frac{0.85–0.91}{\sqrt{\frac{0.91(1-0.91)}{180}}})=P(z>-2.813)=0.9975$

Final answer:
The probability that more than 85% of the sample will be defect free = 0.9975