Question

Problem 96e

Answer 1

Given information

Use the following information to answer the next three exercises. The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

At a  call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses

from one call to the next has the exponential distribution.

Step-by-step explanation

Step 1.

As given in the problem that the average lifetime of a certain new cell phone is three years. And the manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

Therefore,

  

where

  

The decay rate is given by

   

The cumulative distribution function for the exponential distribution is given as follows:

  

Required probability can be calculated as follows:

   

Therefore, the probability that fewer than calls occur within an hour is