Question

97 rental requests arrived over a 26 week span. Assume that everyone rents a pair of skis for one weekend and that Salt Lake City has 5 pairs of rental skis. Also assume no variation in rental times (i.e. the standard deviation of rental times is zero) and that inter-arrival times are exponentially distributed. How long, on average, do customers have to wait for a pair of skis?

A. 1.19 weeks

B. .69 weeks

C. .19 weeks

D. .89 weeks

Answer 1

Here, we have 5 pair of skis available. So,the number of servers available is 5. i.e. k=5

The rate of arrival is 97 customers every 26 weeks. Therefore, =97/26=3.73 customers per week

And it is given that the inter arrival time follows exponential distribution with parameter 3.73 and average inter arrival time 1/=0.2680

=0.019197

The waiting time is given by

=

=

=1.19 weeks