Suppose that over the long run a manufacturing process produces 1% defective items. Use the Poisson approximation to the binomial distribution to calculate the probability of getting two or more defectives in a sample of 200 items.

The probability of getting two or more defectives in a sample of 200 items

0.3233

Step-by-step explanation:

step1:-

The probability of getting 1 percentage defective items is

P(D) =

Given total number of items is n=200

use the Poisson approximation to the binomial distribution that is

λ=np=200(0.01)=2

by using Poisson distribution P(X=r)=

Step2:-

The probability of getting two or more defectives items

using Poisson distribution

on simplification, we get

by using calculator e^-2 value is 0.13533

after simplification

Final -

The probability of getting two or more defectives in a sample of 200 items

0.3233

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