Customers are serviced at a rate of 10 customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than two minutes?
A) less than or equal to 0.25
B) greater than 0.25 but less than or equal to 0.30
C) greater than 0.30 but less than or equal to 0.35
D) greater than 0.35

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\lambda x}$, where $\lambda$ is the rate parameter. In this case, $\lambda = 10$ customers per hour, or $\frac{10}{60} = \frac{1}{6}$ customers per minute. To find the probability that service will require fewer than 2 minutes, we set $x = 2$ minutes. Thus, $P(X < 2) = 1 - e^{-\frac{1}{6} \cdot 2} = 1 - e^{-\frac{1}{3}}$. Evaluating this gives a value greater than 0.25 but less than or equal to 0.30.

Customers Are Serviced at a Rate of 10 Customers Per