Question

Problem 53

Answer 1

Given information

Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution:  

Step-by-step explanation

Step 1.

The cumulative density function of the exponential distribution is given by,

,

 is the decay parameter.

According to the given information, the random variable  denotes the time spent with each customer. This follows the exponential distribution with parameter  

Here, use the following equation with the given value

.

Then, we get 

  

and

 

Therefore,

 

Hence, the value of is .