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

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x