At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes.The car wash takes exactly 4 minutes (this is constant).On average, how many customers would be at the car wash (waiting in line or being serviced)?
A)8.17
B)7.46
C)6.53
D)0.46

Question

Quizplus · Accepted Answer

First, we need to calculate the arrival rate per minute: 
7 cars / 30 minutes = 0.23 cars per minute

Next, we need to calculate the service rate per minute: 
1 car / 4 minutes = 0.25 cars per minute

Then, we can use the formula for the average number of customers in a queuing system: 
L = λ/(μ-λ)

Where λ is the arrival rate and μ is the service rate.

Plugging in the values: 
L = 0.23 / (0.25 - 0.23) = 11.5

This means on average, there are 11.5 cars either being serviced or waiting in line at the car wash. However, since we cannot have half a car, we round down to the nearest integer which gives us 11. Therefore, the closest option given is B, with an average of 7.46 customers.

At an Automatic Car Wash, Cars Arrive Randomly at a Rate