Lesson 4

Lesson 4: Z-Scores

Focus

Over the last three months, a cookie company has had an increase in the number of cookies that are broken and, therefore, need to be thrown out. In other words, these cookies do not meet the minimum quality standard. The more cookies that are thrown out before packaging, the less money the company will make.

The company decides to compare products produced at its four manufacturing facilities to see if the problem is occurring at only one facility or if the problem is occurring at more than one facility. If a problem is found in any facility, the company will then compare products produced by different work shifts to see if the problem is due to human error. Otherwise, if it doesn’t appear to be the fault of one work shift, the equipment needs to be examined for faults.

The normal curve for each of the manufacturing facilities and work shifts will be unique. Each data set will have its own mean and standard deviation. It is likely that the particular data value that the company wants to examine—in this case, the acceptable number of broken cookies—is not exactly one, two, or three standard deviations away from the mean. The company will need another way to analyze the data to help make good business decisions.

In this lesson you will learn about another tool that can be used to compare data, make predictions, and solve problems when dealing with normally distributed data.

This lesson will help you answer the following critical questions:

• How can two or more different normally distributed data sets be compared?
  
  
• How can the area under a normal curve be determined for values that are not exactly one, two, or three standard deviations away from the mean?

Assessment

• Lesson 4 Assignment

All assessment items you encounter need to be placed in your course folder.

Save a copy of the Lesson 4 Assignment to your course folder.

Materials and Equipment

• calculator