2. A quality control inspector for ToolTime Mfg. accepts shipments of parts from
ID: 3070900 • Letter: 2
Question
2. A quality control inspector for ToolTime Mfg. accepts shipments of parts from a particular supplier whenever one or fewer defective parts are found in a sample of ten tems tested. (5 pts each) a. If the proportion of defective parts in the population (T) 0.01, what is the probability of accepting the shipment? b. If the proportion of defective parts in the population () 0.05, what is the probability of accepting a shipment? c. If the proportion of defective parts in the population (T) 0.10, what is the probability of REJECTING the shipment? d. What is the expected value for the number of defective parts for the situation in part a? e. What is the standard deviation of the number of defective parts for the situation in part c?Explanation / Answer
Ans:
n=10
a)P(accept)=P(x<=1)
=P(x=0)+P(x=1)
=(1-0.01)^10+10C1*0.01*(1-0.01)^9
=0.9957
b)P(accept)=P(x<=1)
=P(x=0)+P(x=1)
=(1-0.05)^10+10C1*0.05*(1-0.05)^9
=0.9139
c)P(accept)=P(x<=1)
=P(x=0)+P(x=1)
=(1-0.1)^10+10C1*0.1*(1-0.1)^9
=0.7361
P(reject)=1-0.7361=0.2639
d)Expeceted value=n=10*0.01=0.1
e)standard deviation=sqrt(np(1-p)=sqrt(10*0.1*(1-0.1))=0.95
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