Show work The life of a semiconductor laser at a constant power is normally dist

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The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a standard deviation of 600 hours. a) What is the probability that a laser fails before 5600 hours? Round your answer to four decimal places (e.g. 98.7654) b) what is the life in hours that 90% of the lasers exceed? Round your answer to the nearest integer (e.g. 9876). c) what should the mean life equal for 99% of the lasers to exceed 10000 hours before failure? Round your answer to the nearest integer (e.g. 9876). d) A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently, what should the mean life equal for 99% of the products to exceed 10000 hours before failure? Round your answer to the nearest integer (e.g. 9876).

Explanation / Answer

a)P(X<5600)=P(Z<(5600-7000)/600)=P(Z<-2.33)=0.0099( please try 0.0098 if comes wrong due to rounding)

b)

for top 90 percent ; critical z=-1.28

x=mean+z*std deviaiton=7000-1.28*600=6232 ( please try 6231 if comes wrong due to rounding)

c)

for top 99 percent ; critical z =-2.58

mean =x-z*std deviation =10000+2.58*600=11548

d)let probability laser works=p

probability that system works =P(all 3 component works)=p3 =0.99

p=0.9967

for above probability crtiical z=-2.72

hence mean =10000+2.72*600=11632

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