Problem $10-11($Algo$)$

An engineering firm retains a technical specialist to assist four design engineers working on a project. The help that the specialist gives engineers ranges widely in time consumption. The specialist has some answers available in memory, others require computation, and still others require significant search time. Engineers require assistance, on average, once every $8\mathrm{.}30$ hours. Each assistance takes, on average, $1\mathrm{.}30$ hours. Engineers needing help do not interrupt if the specialist is already involved with another engineer.

Treat this as a finite queuing problem and answer the following questions. In your calculations, use the value of $"x"$ in Exhibit $10\mathrm{.}10$ that is closest to the value you compute.

a$.$ How many engineers, on average, are waiting for the technical specialist for help?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Average number of engineers waiting in line

b$.$ What is the average time that an engineer has to wait for the specialist?

Note: Round your answer to $3$ decimal places.

Average waiting time hours

c$.$ What is the probability that an engineer will have to wait in line for the specialist?

Note: Enter your probability as a decimal $($not percentage$)$ between $0$ and $1$ rounded to three decimal places.

Probability