Determine if the outcome is unusual. Consider as unusual any result that differs

Question

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than µ - 2 or greater than µ + 2

The Acme Candy Company claims that 8% of the jawbreakers it produces actually result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company. Find the Min/Max usual values. Would it be unusual for this sample of 9571 to contain 780 persons with broken jaws?

Explanation / Answer

Ans:

sampling distribution of sample proportions:

mean=0.08

standard deviation=SQRT(0.08*0.92/9571)=0.0028

µ - 2=0.08-2*0.0028=0.0744

µ + 2=0.08+2*0.0028=0.0856

sample proportion=780/9571=0.0815

Not unusual,as 0.0815 lies between 0.0744 and 0.0856.

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