Normal Distribution Calculations BONUS

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

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

Back

Approximately 68% of the data falls within one standard deviation of the mean.

Front

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

Back

Approximately 95% of the data falls within two standard deviations of the mean.

Front

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

Back

Approximately 99.7% of the data falls within three standard deviations of the mean.

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.

Front

What is a z-score?

Back

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

Front

How do you calculate the area under the curve for a z-score of 0?

Back

The area under the curve for a z-score of 0 is 0.5, representing 50% of the data.

Front

What is the area to the left of a z-score of 1.96 in a normal distribution?

Back

The area to the left of a z-score of 1.96 is approximately 0.975, or 97.5%.

Front

If the z-score is 0.75, what is the area to the left of this z-score?

Back

The area to the left of a z-score of 0.75 is approximately 0.7734.

Front

What does it mean if a data set is normally distributed?

Back

It means that the data follows a bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.