Question

Suppose that the probability of a defective part is .05. Suppose that you have a shipment of 800 parts. What is the probability that more than 40 parts will be defective?

please explain how to do this in excel and by hand as if i was just learning this.

Answer 1

by hand

here , probability of a defective part , p = 0.05

n = 800

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since n is very large and p is very small,

binomial distribution can be approximated to poisson distribution with mean =np = 800*0.05 = 40

so, mean number of defects=40

poisson probability distribution formula

P(X=x) = e-λλx/x!

P(X>40) = 1-P(X≤40) =

= 1 - 0.541918178 = 0.458081822
so, answer is 0.4581

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By excel

formula for poisson distribution

=1 - POISSON.DIST(40,40,TRUE)

=0.4581