Big Bang Corporation produces shotgun shells in batches of 300. A sample of 10 i
ID: 3318310 • Letter: B
Question
Big Bang Corporation produces shotgun shells in batches of 300. A sample of 10 is tested from each batch. If more than one defect is found in the sample, the entire batch is tested. The quality control expert at Big Bang Corporation knows from past experience that when production is running smoothly 1% of the shells are actually defective. Use this information and probability and statistics to determine the following: A) Determine the standard deviation of the number of defective shells in the sample and interpret its meaning Would you expect to find 1 or more bad shells in your sample on a regular basis? Why or why not? Determine the number of shells you would have to include in the sample for the expected number B) C) of defective shells to be 1. D) Why do you think Big Bang Corporation tests a sample of only 10 shells? E) Why do you think the Big Bang Corporation has a policy of testing the entire batch (i.e. all 300) if more than 1 defect is found in the sample of 10?Explanation / Answer
A)
Since n=10
And p=0.01
Var(X)=n*p*q=10*0.01*0.99=0.099
SD(X)=0.345
There is 0.345 variability in number of defective pieces from mean number of defective pieces.
B) I think no because probability of getting defective in sample of 10 is very less and mean =0.1 so barely we find any defective piece
C)
E(X)=nP=n*0.01=1 this gives n=100
D)they have to check whole sample if find any defective so Probability of getting defective in sample size of 10 is very less so they have to check less no.of lots if divided into 10
E) because if we get 1 defective in the sample of 10 hence there is chance that there is more number of defective pieces
As E(X)=np=10*p=1 this gives p=0.1
Hence for n=300 E(X)=np=300*0.1=30
So checking whole batch is necessary
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