Question

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes (i.e. the mean number of calls answered in a minute is 1/2.8). What proportion of callers is put on hold longer than 2.8 minutes?

Answer 1

Answer: 0.3679

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

$P(x)=1-e^{-\lambda x}$, where $\lambda$  is the mean of the distribution.

Given :  A mean length of waiting time equal $2.8$ minutes

i.e. Mean number of calls answered in a minute $\lambda=\dfrac{1}{2.8}$

Now, the proportion of callers is put on hold longer than 2.8 minutes is given by :_

$P(x>2.8)=1-P(x$

Hence, the proportion of callers is put on hold longer than 2.8 minutes = 0.3679