Question

The useful life of an electrical component is exponentially distributed with a mean of 5,000 hours.

a. What is the probability the circuit will last more than 5,750 ​hours?

b. What is the probability the circuit will last between 5,000 and 5,250 hours?

c. What is the probability the circuit will fail within the first 4,750 ​hours?

Answer 1

X ~ Exp ()

Where,

Mean = 1 / = 5000 So, = 1 / 5000

a)

P( X > x) = e^-X

So,

P( X > 5750) = e^{-5750 / 5000}

= 0.3166

b)

P(x1 < X < x2) = e^{-x1 -} e^-x2

So,

P(5000 < X < 5250) = e^-5000/5000 - e^-5250/5000

= 0.0179

c)

P( X < x) = 1 - e^-X

So,

P( X < 4750) = 1 - e^-4750/5000

= 0.6133