Question

The probability a telesales represenative making a sale on a customer call is .15. Find the probability: 1. Her first sale comes after 5 calls. 2. Her first 5 calls went with out a sale. What is the probability she will have to make no more than 13 calls until her first sale? 3. Less than 2 sales are made on 5 calls Represenatives are required to make an average of at least 4 sales a day or they are fired. 4. Find the least number calls the represenative is required to make a day so not to be fired. 5. Compute the variance for the number sales made in a day if she makes the minimum number of call to keep her job.

Answer 1

SOLUTION:

From given data,

The probability a telesales represenative making a sale on a customer call is 0.15.

Let ,

X: number of calls to make r sales

p : p[sales on a call]

p : 0.15 and q = 1-p = 1- 0.15 = 0.85

1. Her first sale comes after 5 calls.

p[Her first sale comes after 5 calls] = p[x>5] = 1- p(no.of sales)⁵

= 1-( 0.15 )⁵

p[x>5]= 0.99

2. Her first 5 calls went with out a sale. What is the probability she will have to make no more than 13 calls until her first sale?

p[she has to make more than 13 calls until her first sale] =

  

      

  

  

  

3. Less than 2 sales are made on 5 calls Represenatives are required to make an average of at least 4 sales a day or they are fired

p[Less than 2 sales are made on 5 calls] = p[1 sale is made on 5 calls]

  

  

4. Find the least number calls the represenative is required to make a day so not to be fired.

p[X calls to make is sales] = p[X] = E(r)

X = 4/0.15

= 400/15

= 26.67

At least 27 calls has to be made to make is sales

5. Compute the variance for the number sales made in a day if she makes the minimum number of call to keep her job.

Var[r] if X( minimum number of call to keep her job)

X=27

Var(r) = np(1-p)

= 27*0.15*0.85

= 3.4425

Var(r) = 3.4425 .