A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed.

A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed. Determine:

a.Average number of customers waiting in line.

b.Average time customers spend  in the system.

The average number of customers waiting is 0.196 and average time spend is 0.00862 hr.

Step-by-step explanation:

Given:

Arrival rate, = 64/hr

Service time = 20 sec/cup

Service rate = = per/min = = per/hr

According to the question:

Its a Poisson's distribution of (M/M/1) model.

Formula to be used:

a.Average number of customers waiting in line.

 ⇒  

b.Average time customers spend  in the system.

 ⇒

Solving step-wise:

a.Average no. of customer waiting.

 ⇒  

 ⇒

 ⇒

b.Average time spend.

 ⇒

 ⇒

 ⇒   hr

So the average number of customers waiting is 0.196 and average time spend is 0.00862 hr.

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)