Question

Suppose that the average time a fully charged​ 6-volt laptop battery will operate a computer is 2.8 hours and follows the exponential probability distribution. Determine the following probabilities.

​a) Determine the probability that the next charge will last less than 2.1 hours.

​b) Determine the probability that the next charge will last between 2. ]and 5 hours.

​c) Determine the probability that the next charge will last more than 3.1 hours.

Answer 1

X ~ Exponental ()

Where mean = 1 / = 2.8

So,

= 1 / 2.8

a)

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

P( X < 2.1) = 1 - e^-2.1/2.8

= 0.5276

b)

P(x1 < X < x2) = e^-X1 - e^-X2

So,

P(2 < X < 5) = e^-2/2.8 - e^-5/2.8

= 0.3218

c)

P( X > x) = e^-X

So,

P( X > 3.1) = e^-3.1/2.8

= 0.3305