Answer:
hello your question is incomplete below is the complete question
Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:
(a) lambda=.5
Pr=
(b) lambda=0.9
Pr=
(c) lambda=1.1
Pr=
answer : a) P( X> 5 ) = 0.0821
       b) P( X > 5 ) = 0.0111
       c) P ( X > 5 ) = 0.00409
Step-by-step explanation:
A) P( X > 5 ) = exp ( - λ * x )
  = [tex]e^{-2.5}[/tex] ≈ 0.082
B)  P( X > 5 ) = exp ( - λ * x ) Â
 = [tex]e^{-4.5}[/tex] ≈ 0.0111
C) P( X > 5 ) = exp ( - λ * x ) Â
 = [tex]e^{5.5}[/tex]  ≈ 0.00409
