Question 260100: I am having trouble understanding this. Can someone please help me?
The probabilities that a batch of 4 computers will contain 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, and 0.001 respectively.
a. Set up a probability distribution to describe this situation.
b. Based on these probabilities how many defective computers would you expect to find in this batch? (This would be the mean of the distribution.)
c. How much would this value reasonably be expected to fluctuate? (This is the standard deviation.)
d. What’s the probability of finding at most 2 defective computers in this batch?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The probabilities that a batch of 4 computers will contain 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, and 0.001 respectively.
a. Set up a probability distribution to describe this situation.
The only number missing is zero.
Add the probabilities you are given and subtract that sum from 1 to
get the probability of zero computers being defective.
I get: 1 - 0.9961 = 0.0039
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Now write the ordered pairs:
(0,0.0039),(1,0.6274),etc
That is the probability distribution
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b. Based on these probabilities how many defective computers would you expect
E(x) = 0*0.0039 + 1*0.6274 + 2*0.3102 + etc
to find in this batch? (This would be the mean of the distribution.)
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c. How much would this value reasonably be expected to fluctuate? (This is the standard deviation.)
That is a messy problem unless you have a calculator or software that
will work it for you.
I get std = 0.6108.. using a TI calculator.
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d. What’s the probability of finding at most 2 defective computers in this batch?
P(2<= x <=4) = 1 - [P(x=0 + P(x=1) = 1- [0.0039+0.6274] = 0.3687
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Cheers,
Stan H.
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