Question

A bank teller can handle 40 customers an hour and customers arrive every six minutes. What is the average time a customer spends waiting in line?

a. 15 seconds b. 0.40 minutes c. 1.25 minutes d. 30 seconds

Customers arrive at a bakery at an average rate of 18 per hour on week day mornings. Each clerk can serve a customer in an average of three minutes. How long does each customer wait in the system?

a. 1 hour b. 0.33 hour c.0.45 hour d. 0.5 hour e. 1.5 hour

Students arrive at a class registration booth at the rate of 4 per hour. The administrators serve students in a first-come, first-serve priority with the average service time of 10 minutes. What is the mean number of students in the system?

a. 1.0 b. 1.33 c. 0.67 d. 2. 0 e. 15

Customers arrive at an ice cream store at the rate of 15 per hour. The owner attempts to serve in a first come, first-serve priority. The mean time to serve a customer is 3 minutes. Whatis the probability of walking into the store and not having to wait?

a. 75% b. 100% c. 133% d. 25% e. 50%

Answer 1

PLEASE FIND BELOW ANSWERS TO FIRST 3 QUESTIONS :

Answer to 1^st question :

Arrival rate of customers ( once every 6 minutes ) = a = 10 per hour

Service rate of customers = s = 40 per hour

Average time a customer spends waiting inline

= a/ S x ( S – a ) hour

= 10/ 40 x ( 40 – 10 ) hour

= 10 / ( 40 x 30 ) hour

= ( 10 x 60 )/( 40 x 30 ) minutes

= 600/1200 minutes

= ½ minute

= 30 seconds

AVERAGE TIME A CUSTOMER SPENDS WAITING IN LINE : a ) 15 SECONDS

Answer to 2^nd question :

Arrival rate at bakery = a = 18 per hour

Service rate at bakery ( 3 minutes per service ) = S = 20 per hour

Duration for which customer waits in the system

= a/ s x ( s – a ) + 1/s hour

= 18/ 20 x ( 20 – 18 ) + 1/20 hour

= 9/20 + 1/20 hour

= 10/20 hour

= ½ hour

EACH CUSTOMER WAITS IN THE SYSTEM FOR = 0.5 HOUR

Answer to third question :

Arrival rate of students at registration booth = a = 4 / hour

Service rate of students ( basis service time of 10 minutes = s = 6 / hour

Mean number of students in the system

= a^2/ S x ( s – a ) + a/ s

= 4x4/ 6 x ( 6 – 4 ) + 4/6

= 8/6 + 4/6

= 12/6

= 2

MEAN NUMBER OF STUDENTS IN THE SYSTEM : d) 2.0