Question

A vendor is supplying 120 parts. Suppose that of them are defective. We take a sample of size 10. At least 90% of the time the sample will containk or fewer items. What is the smallest value of K? Give numerical answers as integers or decimals rounded to four decimal places 1. Notice here that the population site is known. We also know that M= of these are defective We are taking a sample of siren- Let X be the number of defective items in the sample. X has a distribution 2 Notice that this is an inverse probability problem. We want to know the smallest value of k where PIXM) 09. Use Dr. Jackson's appropriate calculator function or program to solve this problem. The calculator returns the following portion of the CDF table 20 3 At least 90% of the time the sample will containk or fewer tem What is the value of

Answer 1

1.population size N = 120. M= 6 number of defectives. and we are taking a sample size n=10.

Then X has a hyper-geometric distribution.

To find the smallest k, we will find P(X<=k) for k=1,2,3... and the first time it crosses 0.9 we'll have our k.

We see for k=0, P(X<=k)= P(X<=0) = 0.586.

And for k=1, P(X<=k)=P(X<=1) = 0.92

Answer: k=1.