The useful life of one type of projector lamps has a normal distribution with a

Question

The useful life of one type of projector lamps has a normal distribution with a mean of = 2250 hours and a standard deviation of =175 hours. Use X to denote the life of a projector lamp selected at random.

(H) The lamp manufacturer is planning to offer a warranty on the useful lamp life. If the useful life is less than the warrantied useful life, represented by xw , the manufacturer will offer a free replacement. If the manufacturer wants about 5% of the lamps to be replaced free, the warrantied life xw should be closest to

Explanation / Answer

here as we know that for 5th percentile criitical z score =-1.6449

therefore corresponding value of warrantly =mean +z*std deviation =2250-1.6449*175=1962.15 ~1962 Hours

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