When a truckload of apples arrives at a packing plant, a random sample of 125 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 8% of the sample is unsatisfactory. Suppose that in fact 10 % of the apples on the truck do not meet the desired standard. What is the probability that the shipment will be accepted anyway?
Accepted Solution
A:
Answer: The probability that the shipment will be accepted anyway is 0.2266.Step-by-step explanation:Since we have given that n = 125[tex]\hat{p}[/tex] = 8% = 0.08p = 10% = 0.10First we will find the test statistic value:[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.08-0.10}{\sqrt{\dfrac{0.10\times 0.9}{125}}}\\\\z=\dfrac{-0.02}{0.0268}\\\\z=-0.75[/tex]So, the p-value would be P(z<-0.75)=0.2266Hence, the probability that the shipment will be accepted anyway is 0.2266.