Algebra 2 DLD 18 - 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 is the empirical rule (68-95-99.7 rule)?

Back

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

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

Front

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

Back

The mean is the central point of a normal distribution and determines the location of the peak of the curve.

Front

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

Back

The standard deviation measures the spread of the data around the mean. A larger standard deviation indicates a wider spread of values.

Front

How do you find the percentage of data above a certain value in a normal distribution?

Back

To find the percentage of data above a certain value, calculate the z-score for that value and then use the standard normal distribution table to find the corresponding percentage.

Front

What is the area under the normal distribution curve?

Back

The area under the normal distribution curve represents the total probability, which is always equal to 1.

Front

How do you interpret a z-score of 2?

Back

A z-score of 2 indicates that the value is 2 standard deviations above the mean.