Question

April runs a small shop where she provides a service. She is able to process an average of 11 customers per hour. An average of 7 customers per hour seek this service at her shop. What is:

Answer 1

5. Po= 0.36

6. Pn = 0.04

7. 0.16

8. 1.11

9. 1.75

10. 9.9

Step-by-step explanation:

5. Computation for the probability that April will not be working with a customer

Using this formula

Po=1-(Average number of arrival per hour/Average number of customer served per hour)

Let plug in the formula

Po= 1-(7/11 )

Po=1-0.64

Po= 0.36

Therefore the probability that April will not be working with a customer will be 0.36

6. Calculation for the probability of 5 customers in the system

Using this formula

Pn= (Average number of arrival per hour/Average number of customer served per hour)* Po

Let plug in the formula

Pn= (7/11)^5* 0.36

Pn=0.104358*0.36

Pn=0.037

Pn = 0.04 (Approximately)

Therefore the probability of 5 customers in the system will be 0.04

7. Calculation for the average time a customer spends waiting in line

Time spend Waiting in line=7^2/11(11 – 7) /7

Time spend Waiting in line=(49/44)/7

Time spend Waiting in line = 1.11/7

Time spend Waiting in line= 0.16

Therefore the average time a customer spends waiting in line will be 0.16

8. Calculation for the average number of customers waiting in line

Customers waiting in line = 7^2/11(11 – 7)

Customers waiting in line=49/44

Customers waiting in line= 1.11

Therefore the average number of customers waiting in line will be 1.11

9. Calculation for the average number of customers in the system

Average customers in the system= 1.11 +(7/11)

Average customers in the system= 1.11 +0.64

Average customers in the system = 1.75

Therefore the average number of customers in the system will be 1.75

10. Calculation for the arrival rate in order for April to stay that busy

Arrival rate = 0.9 * 11

Arrival rate = 9.9

Therefore the arrival rate in order for April to stay that busy will be 9.9