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The lifetime of a particular component is normally distributed with a mean of 1000 hours and...

The lifetime of a particular component is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. What is the 80th percentile of component lifetimes? Question 13 options: 84 1254 1157 1084

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Answer #1

X : lifetime of a particular component

X is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours

Let X80 be the 80th percentile of component lifetimes

Therefore,

P(X X80) = 0.80

Z80 be the Z-score of X80

Z80 = (X80 -mean)/Standard deviation = (X80 - 1000)/100

X80 = 1000+100Z80

P(ZZ80) = P(X X80) = 0.80

From standard normal tables,

P(Z0.84) =0.79950.80

Z80 = 0.84

X80 = 1000+100Z80 =1000+100 x 0.84 = 1000+84 = 1084

X80 = 1084

80th percentile of component lifetimes = 1084

Answer : 1084

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