6.4 Flashcard Normal Distributions

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 does it mean if a normal distribution is symmetrical about the mean?

Back

It means that the left and right sides of the distribution are mirror images of each other, indicating that the mean, median, and mode are all equal.

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 standard deviation?

Back

A standard deviation is a measure of the amount of variation or dispersion in a set of values.

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 (or 100%).

Front

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

Back

The mean is the central point of the distribution, where the highest frequency of data points occurs.

Front

What does it mean for data to be one or more standard deviations above the mean?

Back

It means that the data point is greater than the mean plus one or more times the standard deviation, indicating it is in the higher range of the distribution.