Question

The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 13 minutes. (a) What is the probability that there are no calls within a 30-minute interval

Answer 1

P(X>30) = 1 - F(30) = 0.0995

Explanation:

Let X be the exponential distributed random variable of time between the calls with the given mean of 13 minutes

E(X) = 13

As we have the continuous random variable (time), the distribution is

F(x) = 1 - e^(-λx)

Now we need to calculate the λ from the formula of exponential distribution which is

E(X) = 1/λ = 15

So, λ = 1/15

Now, we will calculate the probability that there are no call within 30 minutes time interval, It mean we need to find the probability when time is greater than 30 (X>30)

P (X>30) = 1 - F(30) = 1 - (1 - e^(-30*1/13)

P (X>30) = e^(-30/13) = e^(-2.3) = 0.0995

P(X>30) = 0.0995