Problem 15-7 (algorithmic) speedy oil provides a single-server automobile oil change and lubrication service. customers provide an arrival rate of 4 cars per hour. the service rate is 5 cars per hour. assume that arrivals follow a poisson probability distribution and that service times follow an exponential probability distribution. what is the average number of cars in the system? if required, round your answer to two decimal places

There are 4 average cars in the system.

Step-by-step explanation:

Since we have given that

Arrival rate = λ = 4 cars per hour

Service rate = μ = 5 cars per hour

We need to find the average number of cars in the system.

So, Average number of cars would be

So, it becomes,

Hence, there are 4 average cars in the system.

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85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560