Customers are serviced at a rate of six customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes?
A) less than or equal to 0.70
B) greater than 0.70 but less than or equal to 0.80
C) greater than 0.80 but less than or equal to 0.90
D) greater than 0.90

Question

Quizplus · Accepted Answer

We need to convert the time unit from hour to minutes: 
Six customers per hour $ightarrow$ six customers per 60 minutes. 
Therefore, the rate parameter $\lambda$ of the exponential distribution is $\lambda = 6/60 = 0.1$ customers per minute.

Let X be the time in minutes needed to serve one customer. 
We want to find P(X < 20).

The cumulative distribution function (cdf) of an exponential distribution with rate parameter $\lambda$ is given by 
$F(x) = 1 - e^{-\lambda x}$ for x > 0

Therefore, 
$P(X < 20) = F(20) = 1 - e^{-0.1	imes 20} \approx 0.8187$

So the answer is (C), which corresponds to a probability between 0.80 and 0.90.

Customers Are Serviced at a Rate of Six Customers Per