Lesson 2 Overview

In the previous session, we looked at summary measures of data. Along with the measures of centrality (mean and median), we learned another important concept: variation (measured most often by standard deviation). Variation is inherent in nature; it is so ubiquitous that we often do not even realize it. For example, take your daily commute. Does it take the same amount of time even if traffic and weather conditions did not change? Of course not. If your average commute time is 30 minutes, it probably took you 28 minutes this Monday, 32 minutes on Tuesday, and may be 27 minutes on Wednesday. And on those rare occasions when an irresponsible driver texting while driving causes an accident and massive traffic jam, it may take you up to an hour.  

The topic of variation brings us to our next discussion: uncertainty. Businesspeople must deal with this inherent variation all the time. Think about the auto parts supply chain. Suppliers promise to deliver within a time window, but the exact time of delivery may vary based on factors outside the control of even the most reliable supplier. So, the supply chain managers assess the risk of stockouts and maintain a minimum level of inventory all the time (known as safety stock). Higher/lower levels of risk would mean maintaining higher safety stock levels. If your inventory-carrying costs are high, you would want to be as precise as possible in your assessment of the likelihood of stockout.  

Take another example: staffing decisions at an urban hospital emergency room. Admissions surge on late Friday and Saturday nights. The emergency room currently has three acute care rooms. The emergency room manager would like to know the chance that more than three patients will be admitted in an hour. Long wait times at the emergency room mean that patients suffer. This reflects badly on the hospital, affecting its reputation. If the chance is high, the hospital should invest in the facility and its staff to meet the demand. If the chance is fairly low, it may not make sense to keep expensive resources such as doctors and nurses idle for a significant amount of time. Maybe those resources could be better used somewhere else. 

In other words, due to the inevitable presence of variation in everyday business, we need to evaluate the probability (chance, likelihood, possibility) of something happening. Other times, we want to maintain a certain level of certainty and need to calculate the value of the underlying variable. For example, what is the level of inventory to carry so the chance of stockout is less than 5%? How many acute care rooms and physician-nurse teams should the emergency room have so that no more than 10% of patients wait to be seen by a doctor or nurse? In this session, we learn to make these kinds of decisions using the most important probability distribution: normal distribution. 

Learning Objectives

Upon completion of this lesson, you should be able to

• construct a probability distribution (table and/or graph) and make inferences based on that distribution;
• identify business scenarios where normal distribution is applicable;
• calculate the probability of an event happening (or not happening) using normal and the standard normal (z) distributions; and
• calculate the value of a variable required to maintain a degree certainty of using normal and the standard normal (z) distributions.

To review how the content, activities, and assessments align with one another and the course objectives, please visit the Course Map.

Lesson Readings and Activities

By the end of this lesson, make sure you have completed the readings and activities found in the Course Schedule.