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the quick snap photo machine at the lemon county bus station takes snapshots in exactly 100 seconds. customers arrive at the machine according to a poisson distribution at the mean rate of 25 per hour. on the basis of this information, determine the following:
a. the average number of customers waiting to use the photo machine
b. the average time a customer spends in the system
c. the probability an arriving customer must wait for service

a. 1.92 customer

b. 400 seconds.

c. 0.6944

Step-by-step explanation:

The system described is a waiting line type (M / M / 1) with 100s service time, that is, a service rate mu = 36 customers / hour; and a lambda arrival rate = 25 customers / hour. In this way,

a. The number of customers waiting to use the machine is: lambda ^ 2 / [mu (mu - lambda)] = (25^2) / [36 (36 - 25)] = (25^2) / (36*9) = 1.92 customers .

b. The average time a client spends in the system is: 1 / (mu - lambda) = 1 / (36 - 25) = 1/9 = 0.11 hours = 400 seconds.

c. The probability that a arriving customer should wait for the service is given by: lambda / mu = 25/36 = 0.6944.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: