A manufacturer of halogen bulbs knows that 39% of the production of their bulbs

Question

A manufacturer of halogen bulbs knows that 39% of the production of their bulbs will be defective. Suppose knows that a consumer purchases a package of 300 bulbs. Calculate the mean and the standard deviation of the number of bulbs that can be expected to be defective. Use correct notation. x bar = 9, s = 3.0 mu = 90, sigma = 7.9 x bar = 90, s = 7.9 x bar = 900, s = 295 mu = 9, sigma = 3.0 Would it be unusual for 16 of the bulbs to be defective? Justify your answer. A) No, because 16 is within 3 standard deviations of the mean. B) Yes, because 16 is within 2 standard deviation of the mean. C) No, because 16 is more than 2 standard deviations from the mean. D) No, because 16 is within 2 standard deviations of the mean. E) Yes, because 16 is more than 2 standard deviations from the mean.

Explanation / Answer

p=0.03 and n=300

a) expected number of defective bulbs is n*p=0.03*300=9

b) standard deviation is sqrt(n*p*(1-p))=sqrt(9*0.97)=2.95

16 is not within 2 standard deviations (i.e 9+2*2.95=14.9)

thus answer is E

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