Question

A process for manufacturing an electronic component yields items of which 1% are defective. A quality control plan is to select 100 items from the process, and if none are defective, the process continues. Use the normal approximation to the binomial to find
(a) the probability that the process continues given the sampling plan described;

(b) the probability that the process continues even if the process has gone bad (i.e., if the frequency of defective components has shifted to 5.0% defective)

Answer 1

Answer:

0.3830,0.6170

Step-by-step explanation:

Given that a process for  manufacturing an electronic component yields items of which 1% are defective.

n =100 and p = 0.01

Here X no of defectives is binomial since independence and two outcomes.

Approximation to normal would be

X is N($100(0.01) , \sqrt{100(0.01)(0.99)} )$

X is N(1,0.995)

a) the probability that the process continues given the sampling plan described

= $P(X=0)$

(with continuity correction)

=$P(|x|$

b) the probability that the process continues even if the process has gone bad (i.e., if the frequency of defective components has shifted to 5.0% defective)

1-0.3830

=0.6170