00:01
So let us start with the concept which we are going to use here for this question.
00:08
So average number of any objects that were into the system can be given by n is equals to lambda over mu minus lambda.
00:21
Now what are the lambda and mu factors that we will get throughout the question.
00:26
So basically we have given that 5 cars per hour is the arrival rate which indicates basically the value of lambda that is 5 cars per hour arrival rate.
00:42
Then mu is the service rate which we have given according to question as 6 cars per hour that is the service rate.
00:53
So arrivals follow a poisson's distribution.
00:58
Servitrate follows a exponential distribution.
01:02
So according to this in the first part we need to find the average number of cars in system cars in the system.
01:12
So this can be calculated by the formula as we have written in the concept n is equals to lambda over mu minus lambda that will be equals to 5 by 6 minus 5 that will be equals to 5.
01:29
So this will become the required answer for a part.
01:34
Now same in b part we have to find the average time a car waits for wash to begin.
01:42
So let's suppose t be the average time a car waits for the wash to begin.
01:52
So it can be given by the formula t is equals to lambda that is arrival rate over the arrival rate lambda into the bracket the service rate mu minus of arrival rate lambda...