A conveyor belt in a quality control station, brings in randomly selected items

Question

A conveyor belt in a quality control station, brings in randomly selected items from the production line (the number of items brought in the control station is not known.) The items on the conveyor belt are inspected and tested for quality standards and removed from the belt if they fail the tests. It is established that on average 250 items fail the test each day. Determine the probability that in a given day more than 300 items fail the quality control tests. fewer than 200 items fail the quality control tests.

Explanation / Answer

here mean failure in a day =250

and std deviation of failure =(250)1/2 =15.8114

hence by normal approximation of above

a) P(X>300)=1-P(X<=300)=1-P(Z<(300.5-250)/15.8114)=1-P(Z<3.1939)=1-0.9993=0.0007

b)P(X<200)=P(Z<(199.5-250)/15.8114)=P(Z<-3.1939)=0.0007

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