A company in Mexico produces approximately 12 million marbles per day, which is

Question

A company in Mexico produces approximately 12 million marbles per day, which is approximately 90% of the world's marble production. One particular marble product has an engineering specification on the mass that is 40 g plusminus 0.10 g. Their production is normally distributed with a mean of 39.98 g and a standard deviation of 0.041 g. Do the following: a) Calculate the expected percentage of conforming ("good") parts. b) Calculate the expected percentage of parts below the Lower Spec Limit. c) Calculate the expected percentage of parts above the Upper Spec Limit. d) Given these expected defect rates, and assuming similar rates for all their marble products, how many defects are they expected to generate on a daily basis?

Explanation / Answer

a) for expected proportion of conforming parts =P(39.9<X<40.1)=P((39.9-39.98)/0.041<Z<(40.1-39.98)/0.041)

=P(-1.9512<Z<2.9268)=0.9983-0.0255 =0.9728

therefore expected percentage of conforming parts =97.28%

b)expected percentage of parts below lower spec =P(X<39.90) =P(Z<-1.9512) =2.55%

c)expected percentage of parts above upper spec=P(X>40.1)=P(Z>2.9268)=99.83%

d) expected defect percentage =100-97.28% =2.72%

therefore expected defects =np =12 million *2.72% =326400 (approx)

please revert for any clarification required

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