Normal Distribution

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 is the empirical rule?

Back

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

Front

What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

68%.

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

95%.

Front

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

Back

99.7%.

Front

If the mean GPA of a high school is 2.9 and the standard deviation is 0.6, what percentage of students have a GPA between 2.3 and 3.5?

Back

68%.

Front

If the mean number of accidents per week is 6.4 and the standard deviation is 1.5, what proportion of weeks would you expect to have more than 7 accidents?

Back

0.3446.

Front

If the mean number of accidents per week is 6.4 and the standard deviation is 1.5, what proportion of weeks would you expect to have less than 5 accidents?

Back

0.1762.

Front

In a normal distribution, what does the mean represent?

Back

The mean represents the average value of the data set, where the highest point of the curve is located.

Front

What is the significance of standard deviation in a normal distribution?

Back

Standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.