Question

1-Orders come to a warehouse facility with an exponentially distributed interarrival time of 20 minutes. What is the probability of having no orders during a given hour period?

Answer 1

GIVEN:

  Orders come to a warehouse facility with an exponentially distributed interarrival time of 20 minutes.

TO FIND:

The probability of having no orders during a given hour period

SOLUTION:

In the given problem, the number of order arrivals per hour follows poisson distribution with probability density function,

where ​ is the mean number of arrivals per hour (mean arrival rate per unit time) and we know that the inter-arrival time ​ follows exponential distribution which is equal to 20 minutes per order.

Now we will calculate ​ using inter arrival time and find the probability of having no orders during a given hour period using probability density function of poisson distribution.

   Inter arrival time =

Thus mean number of arrivals per hour ​is .

PROBABILITY OF HAVING NO ORDERS DURING GIVEN HOUR PERIOD:

The probability of having no orders (x=0) during a given hour period with mean arrival rate is given by,

  

  

Thus the probability of having no orders during a given hour period is 0.95.