The lifetime of a warning lamp on a piece of equipment is no

The lifetime of a warning lamp on a piece of equipment is normally distributed with 8.20 years and standard deviation 1.40 years. a) What is the probability that the lamp will last more than 10.00 years? b) A particular lamp lasts 8.00 years. What percentile is this lamp on? c) Find the 60^th percentile of the lifetimes. d) What is the probability that the lifetime of lamp is between 9.00 and 11.00 years?

Solution

Let X be the lifetime of a warning lamp

mu = 8.20 and sigma = 1.40

a) Prob that lamp will last more than 10 years

= P(X>10) = P(Z>1.8/1.4=1.29) =

0.5-0.4015 = 0.0985

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b) X = 8 years mean Z = -0.2/1.4 = -0.14

percentile = 50-5.57 = 44.43

c) 60th percentile is z = 0.255

x = 8.20+0.255(1.4)

= 8.557

d) P(9<x<11) = P(0.57<z<2)

=0.4772- 0.2157

= 0.2615