Question

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 25 minutes, what is the probability that X is less than 28 minutes

Answer 1

0.674

Explanation:

Given that :

Average value (m) = 25

P(x < 28) = ∫1/m * e^-x/m (interval 28 to 0)

P(x < 28) = ∫1/25 * e^-x/25 (interval 28 to 0)

P(x < 28) = 1/25( (e^-x/25) / (- 1 / 25))(interval 28 to 0)

1/25( (e^-x/25) * (- 25/ 1)) (interval 28 to 0)

(e^-x/25) x = 28 ; x = 0

e^(-0/25) - e^(-28/25)

e^0 - e^(-28/25)

1 - 0.3262797

= 0.6737202

= 0.674