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Continuous distributions

Study hours and the normal curve

A continuous random variable can take any value in a range: the hours you study in a week might be 3, 3.5, or 3.27. Because no single exact value has a probability, we describe it with a smooth curve, and probability is the area under the curve.

Pick a core class. You'll see a normal distribution for its weekly study hours, then use the 68-95-99.7 rule to read probabilities and percentiles off it.

Your choice isn't recorded anywhere.

Your class:
The normal distribution

Weekly study hours for

Let X be the number of hours you study for in a week. Suppose X is normally distributed:

Note: these numbers were made up and do not represent actual hours spent on each course, real or imagined!

The shaded curve shows where study hours fall. Each band is one standard deviation wide, labelled with the share of students it holds:

68% of values lie within 1σ of the mean · 95% within 2σ · 99.7% within 3σ

Your class:
Using the rule

Read probabilities and percentiles off the curve

Percentiles line up with standard deviations from the mean. Use the curve below.

Note: these numbers were made up and do not represent actual hours spent on each course, real or imagined!

Recap

What makes a continuous distribution