Question

A manufacturer produces test tubes from two independent processes. Process 1 produces

10% defectives while Process 2 produces 15% defectives. Random samples of size 100

are obtained from each process on a daily basis. What is the probability that the sample

from Process 1 has fewer defectives than the of Process 2?

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Answer #1

The number of defectives out of 100 from process 1 has Binomial distribution with . The normal approximation is

The number of defectives ​​​​​​​ out of 100 from process 2 has Binomial distribution with . The normal approximation is

Since and are independent, .

The required probability is

​​​​​​​

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