What is the probability of having to critically review the automobile company even though the actual fraction of high emission samples for that month is still only 10%? b) If the actual fraction of high emission samples remains at 10%, what is the probability that the next critical review will take place in exactly 6 months?

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Of all the registered automobiles of a certain automobile company, 10% violate the state

emissions standard. Each month twelve automobiles are selected at random to undergo an

emissions test. Let N12 be the number of samples which violate the state emissions standard.

If the value of N12 exceeds its mean by more than two standard deviations, the automobile

company is critically reviewed.

a) What is the probability of having to critically review the automobile company even though

the actual fraction of high emission samples for that month is still only 10%?

b) If the actual fraction of high emission samples remains at 10%, what is the probability that

the next critical review will take place in exactly 6 months?

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