Probability Question (Help Please)

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• Feb 19th 2010, 11:09 AM
KyKy
Probability Question (Help Please)
Hey i need help on this question, after reading the book it doesn't give any helpful advice on how to solve this problem, or how to do it.

When a truckload of apples arrives at a packing plant, a random sample of 150 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. Suppose that in fact 8% of the apples on the truck to not meet the desired standard. What's the probability that the shipment will be accepted anyways?
• Feb 19th 2010, 12:23 PM
vince
Quote:

Originally Posted by KyKy
Hey i need help on this question, after reading the book it doesn't give any helpful advice on how to solve this problem, or how to do it.

When a truckload of apples arrives at a packing plant, a random sample of 150 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. Suppose that in fact 8% of the apples on the truck to not meet the desired standard. What's the probability that the shipment will be accepted anyways?

5%*150 = 7.5 defects.

Let X be a binomial random variable; the number of defective apples found.

Use a binomial distribution with p=8% and compute
$P(shipment\;will\; not\; be\; rejected) =P(X\leq{7}) = \sum_{k=0}^{7}\binom{150}{k}(.08)^k(.92)^{150-k}$
• Feb 19th 2010, 12:33 PM
vince
one thing that's bugging me about using a binomial here is that once we find a defective apple, the remaining number of defective apples in the shipment is lessened -- we're not replacing the defective apples to keep the proportion the same throughout the trials. i think im wrong actually, but close. let me now consider poisson.
• Feb 19th 2010, 01:00 PM
vince
nah...since these are independent trials, the realization of a defective apple doesnt propagate to affect the probabaility of the next trial's outcome. i think it's fine as is. i get the prob is ~8%. poisson would work here too since 150*.08 isn't large...