Consider a large population with defect ratio of 1%. We draw a large number of s

Question

Consider a large population with defect ratio of 1%. We draw a large number of samples, each of size 25 and count the number of defective items in each sample. Let DI denote the number of defective items found in sample i, i = 1, 2, . . .N, where N 1. Estimate the median, first quartile and third quartile of the sequence D1 ,D2 , . . . ,Dn.

I submitted this before and was given an answer using the standard normal approx., but I was taught that a good rule of thumb is to use the normal approximation only if np>10 and np(1-p)>10. If n is 25 and p is 0.01, then np is not greater than 10, so the standard normal approx. is not applicable. How to calculate this?.

Explanation / Answer

Ans:

n=25,p=0.01

p(k)=BINOMDIST(k,25,0.01,FALSE)

For,median

P(X<=k)=0.5

For First quartile

P(X<=k)=0.25

For third Quartile

P(X<=k)=0.75

Median,first quartile and third quartile will be equal to=0

k p(k) cumulative prob=P(X<=k) 0 0.7778 0.7778 1 0.1964 0.9742 2 0.0238 0.9980 3 0.0018 0.9999 4 0.0001 1.0000 5 0.0000 1.0000

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