Let X = the time (in minutes) that a postal clerk spends with her customers.This time is known to have an exponential distribution with an average of 4 minutes.What is the probability that the clerk spends 4 to 5 minutes with a randomly selected customer?
A) 0.7135
B) 0.6321
C) 0.3456
D) 0.0814

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $f(x) = \lambda e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}} = \frac{1}{4}$. The probability that X is between 4 and 5 minutes is found by integrating the density function from 4 to 5, which gives $P(4<X<5) = e^{-4/4} - e^{-5/4} = e^{-1} - e^{-5/4}$. Calculating this gives approximately 0.0814.

Let X = the Time (In Minutes) That a Postal