The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a Mean of 13. What is the probability that the arrival time between customers will be 12 or less? Report your answers in decimals, using 4 decimals.

The probability that the arrival time between customers will be 12 or less is 0.6027.

Step-by-step explanation:

We are given that the time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a Mean of 13.

Let X = time between arrivals of customers

The probability distribution for exponential distribution is given by;

where, = parameter of this distribution or the arrival rate

Since, the mean of exponential distribution = E(X) =  

So, 13 = ,

So, X ~ Exp( )

Now, to find the less than or greater than probabilities in exponential distribution we use the Cumulative distribution function of exponential function, i.e.;

So, probability that the arrival time between customers will be 12 or less is given by = P(X 12)

            P(X 12) =

                            =

                            = = 0.6027

Therefore, probability that the arrival time between customers will be 12 or less is 0.6027.