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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?

Respuesta :

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% = 0.08

p = 10% = 0.10

First 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)=0.2266

Hence, the probability that the shipment will be accepted anyway is 0.2266.

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