The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. A) What is the probability that the CPU fails within three years? (6 points) (Round your answer to 4 decimal places)
B) Assume that your corporation owned 10 CPUs, and assume that the CPUs fail independently. What is the probability that at least one fails within three years? (8 points) (Round your answer to 4 decimal places)

0.393 ; 0.9933

Step-by-step explanation:

Given that :

Mean lifetime follows an exponential distribution (m) = 6

a. What is the probability that the CPU fails in the next three years?

Using the poisson distribution formula :

1 - e^-λt

λ = 1/m = 1 / 6 = 0.1667

Probability of failure in next 3 years :

P(X < 3) = 1 - e^-λx

P(X < 3) = 1 - e^-0.1667*3

P(X < 3) = (1 - e^-0.5)

P(X < 3) = 1 - 0.6065306

P(X < 3) = 0.3934693

= 0.3935

b. Assume that your corporation has owned 10 CPUs for three years, and assume that the CPUs fail independently. What is the probability that at least one fails within the next three years?

Number of pc owned = 10

CPU failure is indepndent

Probability of atleast one fails :

1 - P(X ≥ 3)^n

P(X ≥ 3) = 1 - P(X < 3)

P(X ≥ 3) = 1 - 0.3935 = 0.607

Hence,

1 - P(X ≥ 3) = 1 - 0.6065^10

1 - P(X ≥ 3) = 1 - 0.0067345

1 - P(X ≥ 3) = 0.993265

= 0.9933

6x = 48

i hope this . 6 cards each and a total of $48. dvide each side by 6 and you will have your answer.

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation: