what is the approximate probability that fewer than 175 chips will be defective?

Question

Each computer chip made in a certain plant will, independently, be defective with probability .2. If a sample of 1,000 chips is tested, what is the approximate probability that fewer than 175 chips will be defective?

Answer 1

If you want the exact answer, you can use the Binomial distribution with the following parameters:

n=1000

p=0.2

P(X < 175) = P(X <= 174) = use binomcdf command on a TI-84 calculator to find that the exact answer is 0.0206

If you wanted to find an approximate answer, you can use a Normal Approximation to the Binomial Distribution with a discrete value to a continuous value adjustment.

Mean = np = 1000(0.2) = 200

Standard Deviation = square root of (npq) = sqrt(1000*.20*..80) = 12.64911064

Then use normalcdf command on the calculator P(X<175) = P(X<=174.5) = normalcdf(lower bound = 0, upper bound = 174.5, mean = 200, standard deviation = 12.64911064) =

The approximate answer is 0.0219

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