The Water Wheelies production process is designed to produce at most 10 percenta

Question

The Water Wheelies production process is designed to produce at most 10 percentage defective items. Once each day a sample of 100 items is selected, and the number of defective items is determined. If this number is 15 or less, production is continued. Otherwise, production is stopped for equipment maintenance. Suppose that the process is producing defectives at a rate of 20 percentage, but management does not know this fact. After the day's sampling, what is the probability that production will be erroneously continued?

Explanation / Answer

let=x is defective and here n=100

since 20% producing are defectives

p=0.2

so E(x)=n*p=0.2*100=20

Variance(x)=np(1-p)=100*0.2*(1-0.2)=16

sd(x)=sqrt(16)=4

since x<=15, the production will contiue

so errornous probability=P(15<X<20)=P(0<Z<1.25)=P(Z<1.25)-P(Z<0)=0.8944-0.5=0.3944

for X=15, the standard normal variate z=(X-E(x))/sd(x)=(20-15)/4=1.25

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