Intro to 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 are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of data falls within one standard deviation of the mean.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average value of the dataset and is the center point of the normal distribution.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

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

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

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

Back

Approximately 99.7%.

Front

How do you calculate the interval for approximately 95% of data in a normal distribution?

Back

The interval is calculated as: Mean ± 2(Standard Deviation).

Front

If a factory's machine has a mean weight of 1150 pounds and a standard deviation of 22 pounds, what is the weight interval for 95% of molds?

Back

1106 to 1194 pounds.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.