You are manager of a ticket agency that sells concert tickets. You assume that people will call 4 times in an attempt to buy tickets and then give up. Each telephone ticket agent is available to receive a call with probability 0.1. If all agents are busy when someone calls, the caller hears a busy signal. Find , the minimum number of agents that you have to hire to meet your goal of serving 98% of the customers calling to buy tickets.

10 Operators

Step-by-step explanation:

Given:

- The probability that a call is received p = 0.1

- Total number of tries till no call is received  = 4

- Total number of operators required = n

Find:

The minimum number of agents that you have to hire to meet your goal of serving 98% of the customers calling to buy tickets.

Solution:

- We know that each caller is willing to make 4 attempts to get through. An attempt is  a failure if all n operators are busy, which occurs with probability:

                                      (1 - p)^n = q ( failure probability)

- Assuming  call attempts are independent, a caller will suffer four failed attempts with probability:

                                     ( 1 - p )^4n = q^4

- Now, we are given that we want to serve 98% of the customers. Hence, we have the tolerance of only 2% to fail per call. Hence, we can set an inequality as follows:

                                      ( 1 - p )^4n = q^4 < 0.02

- Plug in the values and solve:

                                      ( 1 - 0.1 )^(4n) < 0.02

Taking natural logs:

                                      4n*Ln(0.9) < Ln(0.02)

                                         n > 37.1298 / 4

                                          n > 9.28 ≈ 10

- Hence, the minimum number of operators should n = 10 to meet the quality standards.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .