Question

On average a certain computer part lasts ten years. The length of time the computer part lasts is exponentially distributed .

i)What is the probability that a computer part lasts more than 7 years?

ii) What is the probability that a computer part lasts between 9 and 11 years?

iii)Eighty percent of computer parts lasts for how long?

Answer 1

for exponential distribution:

$P(X<x)=1-e^{-mx}$

we have: $m=1/10$

a)

$P(X>7)=e^{-0.1\cdot7}=0.4966$

b)

$P(9<X<11)=P(X<11)-P(X<9)=e^{-0.9}-e^{-1.1}=0.0737$

c)

$1-e^{-0.1x}=0.8$

$x=-ln0.2/0.1=16.1$ years