SOLUTION: When a truckload of apples arruves at a packing plant, a random sample of 250 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be re
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Question 575462: When a truckload of apples arruves at a packing plant, a random sample of 250 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Although it is not known, in fact 8% of the apples on the truck do not meet the desired standard. What is the probability that the shipment will be accepted anyway?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of combinations of things taken at a time and is calculated by !})
You need the probability of 0 plus 1 plus 2 plus ... plus 11 plus 12 out of 250 trials at a probability of 0.08 for success on any given trial. Hence:
\ =\ \sum_{i\,=\,0}^{12}\left(250\cr\ \ i\right\)\left(0.08\right)^i\left(0.92\right)^{250\,-\,i})
Now I don't care who you are, that is some pretty ugly arithmetic. If you are a really big glutton for punishment, have at it. But here is a much easier way:
Open an Excel spreadsheet (or Numbers if you are using a Mac). Enter the following in any convenient empty cell:
=BINOMDIST(12,250,0.08,true)
And hit "Enter"
3 decimal places is probably way more precision than you need.
John
My calculator said it, I believe it, that settles it
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