Question

2- On the average, a certain type of laptop works effectively for nine years. The length of time this certain laptop works effectively is exponentially distributed.

a) (5%) What is the probability that a the laptop work effectively more than 6 years?

b) (8%) Eighty percent of computer parts last at most how long?

Answer 1

a)

here for exponential distribution parameter β = 9

probability that a the laptop work effectively more than 6 years :

P(X>6)=1-P(X<6)=1-(1-exp(-6/9))=0.5134

b)

pth percentile =-β*ln(1-p)

therefore 80th percentile =-9*ln(1-80/100)=14.485 years