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 of the mean.

Front

What does the area under the normal curve represent?

Back

The area under the normal curve represents the total probability of all outcomes, which equals 1.

Front

How do you find the area to the right of a z-score in a standard normal distribution?

Back

To find the area to the right of a z-score, you can look up the z-score in a standard normal distribution table and subtract the table value from 1.

Front

What is a z-score?

Back

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations.

Front

If z = -2.67, what is the area to the right of this z-score?

Back

The area to the right of z = -2.67 is approximately 0.9962.

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central point of a normal distribution, where the highest point of the curve occurs, and it divides the data into two equal halves.