Lesson 5

Lesson 5: Solving Problems Using the Normal Distribution

 

Focus

 

 

Most companies that produce a product have a quality control department. The department’s responsibility is to make sure the products that are being made meet specifications and are safe.

 

Quality control technicians can be found in a variety of different settings. In a beverage plant, the quality control technician may systematically sample bottles to ensure that the contents are within the acceptable range (e.g., 298.5 to 301.5 mL). In a tire factory, a quality control technician may perform a variety of tests on tires that are produced to make sure that the batch of rubber used to make the tires is good. In a wastewater treatment plant, a quality control technician may test the dissolved oxygen content of the water leaving the plant to make sure it is safe and meets environmental standards.

 

Quality control departments need to be confident in the decisions that are made. An error could result in a product that is not safe or that does not meet the company’s standards reaching the consumer or being released into the environment. Incorrect decisions or changes made to the process can be very expensive for the company.

 

Z-scores and the standard normal distribution can be used by quality control departments to analyze a process. This information can help companies make decisions about their processes and help identify places where changes may need to occur.

 

This lesson will help you answer the following critical questions:

• How can the area under a normal curve be determined between two data values?

• How can you determine a data point when given only the mean, standard deviation, and area under the normal curve?

• How can z-scores be used to solve problems involving normal distributions?

Assessment

• Lesson 5 Assignment

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

 

Save a copy of the Lesson 5 Assignment to your course folder.

 

Materials and Equipment

• calculator