Normal Curve

Front

What is a normal curve?

Back

A normal curve, also known as a Gaussian distribution, is a bell-shaped curve that represents the distribution of a set of data where most values cluster around a central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

What are the two types of standard deviation?

Back

Population standard deviation and sample standard deviation.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95%.

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Front

If a data set is normally distributed, what does the area under the curve represent?

Back

The area under the curve represents the total probability, which equals 1 (or 100%).

Front

In a normal distribution, what is the relationship between the mean, median, and mode?

Back

In a normal distribution, the mean, median, and mode are all equal and located at the center of the curve.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations of the mean.

Front

How do you calculate the z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score tell you?

Back

A z-score indicates how many standard deviations an element is from the mean.