• Understand the properties and characteristics of the standard normal distribution.
• Calculate probabilities and percentiles using normal distribution and [latex]z[/latex]-scores with technology.

The Normal Distribution

Cholesterol and triglycerides are classified lipids or fats. These fats are important for cell health, but they can be harmful when they build up in the blood. Sometimes they can lead to clogged, inflamed arteries, a condition called atherosclerosis. This may keep your heart from working normally if the arteries of your heart muscle are affected.^[1]

The amount of cholesterol in a person’s blood plays an important role in the health of their heart and blood vessels. Most adults have their cholesterol levels checked at least every five years. To help guide treatment, medical organizations have established guidelines that define which cholesterol levels are considered healthy.^[2]

Cholesterol levels for adults in the United States are normally distributed, so normal distribution is a useful tool in evaluating cholesterol levels. According to the Centers for Disease Control and Prevention (CDC), the mean cholesterol level for U.S. adults is [latex]191[/latex] milligrams of cholesterol per deciliter of blood (mg/dL), with a standard deviation (SD) of [latex]40.7[/latex].^[3] There are [latex]3[/latex] ranges used by doctors as a general guidelines for total cholesterol in adults: Normal (Less than [latex]200[/latex] mg/dL), Borderline high ([latex]200[/latex] to [latex]239[/latex] mg/dL), and High (At or above [latex]240[/latex] mg/dL).

Let’s use the CDC data to calculate some probabilities.

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