3. The CPU of a personal computer has a lifetime that is exponentially distribut

Question

3. The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. If you buy 10 CPUs, find the probability that they all last longer than seven years. (ay8.575×10-6 (b) .9760 (c) .0240 (d) .0734 (e) 2.840 x 10-4 4. The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. If a company buys 500 CPUs, find the approximate probability that between 100 and 150 of them (inclusive) last longer than 7 years. G- (a)3085 (b) 4317 (c) .3553 (d) .4629 (e) .5525

Explanation / Answer

3) here probability that one CPU last longer then 7 years =P(X>7) =e-7/6 =0.3114

therefore probability that all 10 last longer then 7 years =(0.3114)10 =8.575*10-6

4)

from central limit theorum ;samplind distribution of sample size 500 is approximately normal

with mean =np =500*0.3114 =155.7016

and std deviaiton =(np(1-p))1/2 =10.3545

hence probability that between 100 and 150 of them last longer then 7 years

=P(100<=X<=150)=P((99.5-155.7016)/10.3545<Z<(150.5-155.7016)/10.3545)

=P(-5.40<Z<-0.5)=0.3085-0.0000 =0.3085

please revert for any clarification required,

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