Probability and Statistics

Approximately 95% of all the data in a normal distribution lie within ___ standard deviations of the mean.

2

Approximately 99.7% of all data in a normal distribution lie within ___ standard deviations of the mean.

3

What is the shape of a normal distribution?

Bell shaped

Normal curves are _________ mathematical models that describe a wide variety of experiments and natural occurrences and have special properties that allow the assignment of probabilities to outcomes.

Bell shaped

Normal curve never touches the ____.

Horizontal axis

Empirical rule

In normally distributed data, about 68% of the data is within one standard deviation of the mean, 95% of the data is within two standard deviations of the mean, and 99.7% of the data is within three standard deviations of the mean. (68-95-99.7 rule)

Approximately 68% of all the data in a normal distribution lie within ___ standard deviation of the mean.

1

The area under a normal curve is ____.

1

Normal curve

the curve representing a normal distribution

The mean, median, and mode all occur at the ____ of a normal distribution.

Peak

What letter represents the mean of a normal distribution?

The lowercase Greek letter, mu. Half the data are above it, half are below it.

What letter represents the standard deviation of a normal distribution?

The lowercase Greek letter, sigma.

What percent of the data in a normal Distribution are more than 3 standard deviations away from the mean?

in a normal distribution, about 0.3% of the data are more than 3 standard deviations away from the mean. The corresponding areas on the graph are so small (each 0.15% of the distribution) you can hardly see it.

Normal distribution

bell-shaped distribution, centered on the mean