Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

What is the average number of cars in the system?

Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

What is the probability that there are exactly 2 cars in the system?

Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

What is the probability that there are no cars at the window?

Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

What percentage of the time is the postal clerk busy?

A random variable $X$ is exponentially distributed with a probability density function of $f(x)=$ $5 e^{-5} x$. Calculate the mean and the standard deviation of $X$.

Using a graphical solution procedure to solve a maximization problem requires that we:

a) move the iso-profit line up until it no longer intersects with any constraint equation.

b) move the iso-profit line down until it no longer intersects with any constraint equation.

c) apply the method of simultaneous equations to solve for the intersections of constraints.

d) find the value of the objective function at the origin.

What is the expected value of a continuous random variable? What is the expected value of an exponentially distributed random variable?

Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation.

What is the average time that a customer must wait before reaching the operator?

A random variable X is normally distributed with mean 20.5 and standard deviation 4.3. Find: $\mathrm{P}(18 \leqslant X \leqslant 22)$

The number of cars that arrive at a bank's drive-through window between 3:00 P.M. and 6:00 P.M. on Friday follows a Poisson process at the rate of 0.41 car every minute. Compute the probability that the number of cars that arrive at the bank between 4:00 P.M. and 4:10 P.M. is:

Exactly four cars. Interpret this result.

The three process regions in a process-chain-network diagram are:

a) manufacture, supplier, customer

b) direct and surrogate, customer, provider

c) independent, dependent, customer interaction

d) direct interaction, surrogate interaction, independent processing

Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation.

What is the probability that the operator is busy?

Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation.

What is the average number of calls waiting to be answered?

Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. Compute the following:

The average amount of time a dog spends waiting in line and being vaccinated.