# What is the probability that exactly six patients will arrive in the next 90 minutes?

Health sciences and medicine

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CHAPTER 6 DISCUSSION QUESTIONS

Create a process ﬂow based on your observation of one of the following:

Patients at the student health center on campus.

Patients at a local ophthalmologist’s oﬃce.

Patients at a local hospital emergency department.

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Order Paper NowFor each distribution listed, provide an example from your work that may be modeled using that distribution. You may not use any examples mentioned in this chapter.

Multinomial distribution

Poisson distribution

Exponential distribution

Normal distribution

Use Excel to create the following probability distributions. Graph your results using a scatter plot.

Normal distribution

Multinomial distribution

For the scenario that follows, solve by hand and then solve using the Excel functions POISSON and EXPONDIST.

The time between arrival of patients to an urgent care center follows an exponential distribution with a mean of 30 minutes.

What is the probability that exactly six patients will arrive in the next

90 minutes?

What is the probability that at least two patients will arrive in the next

60 minutes?

What is the probability that no patients will arrive in the next

60 minutes?

Provide the Excel code needed to generate a random number between [2,4). In Excel, generate 100 random numbers in this interval. Count the number between [2,3) and the number between [3,4). Comment on the results of your count.

Conduct Internet research to determine three feasible alternative packages you might employ for discrete-event simulation. Rate the packages based on documented ease of use, cost, and ability to simulate health care scenarios.

Explain the diﬀerences between discrete-event simulation and Monte Carlo simulation. Provide an example of at least one situation from a health care arena when discrete-event simulation would be preferred and one when Monte Carlo simulation would be preferred.

Suppose we know that the average number of customers present in a queuing system is 10 and the average number of customers waiting in line is 4. Given that the average number of arrivals entering the system per hour is 20, determine the average time a customer spends in the system and the average time a customer spends in line. Be sure to provide appropriate units for your answer.

Each Tuesday, the new residents at an inpatient rehabilitation clinic must visit the medication lab and have all of their existing medications inventoried when they arrive. The interarrival times of patients to the medication lab follow a uniform distribution with an upper bound of 45 minutes and a lower bound of 30 minutes. The service times to have their medication logged follow a normal distribution with a mean of 20 minutes and a standard deviation of 5 seconds.

Using Excel, determine queuing and service statistics for the 40 patients who visit the medication lab over a one-day period. The columns of data you will need to generate include patient ID, interarrival time, arrival time, service start time, wait time, service time, service completion time, time in system, and server idle time.

Calculate the following summary statistics for question 9:

Number of patients who wait

Probability of waiting

Average wait time

Maximum wait time

Percentage of time server is busy

Number waiting > 1 minute

Probability of waiting > 1 minute

Average number of patients in line