The caller times at a customer service center has an exponential distribution with an average of 22 seconds. Find the probability that a randomly selected call time will be less than 30 seconds? (Round to 4 decimal places.)

The probability that a randomly selected call time will be less than 30 seconds is 0.7443.

Step-by-step explanation:

We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.

Let X = caller times at a customer service center

The probability distribution (pdf) of the exponential distribution is given by;

Here, = exponential parameter

Now, the mean of the exponential distribution is given by;

Mean =    

So,    ⇒

SO, X ~ Exp()  

To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;

     ; x > 0

Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)

        P(X < 30)  =  

                         =  1 - 0.2557

                         =  0.7443