Honors - Normal Distribution review graded classwork

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 of all data points and is the center 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

How do you calculate the z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

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

Front

How do you find the probability of a range of values in a normal distribution?

Back

Use the z-scores to find the corresponding probabilities from the standard normal distribution table.

Front

What is the probability of a value being greater than the mean in a normal distribution?

Back

The probability of a value being greater than the mean is 0.5 or 50%.

Front

If the mean is 10.5s and the standard deviation is 0.4s, what is the z-score for 10.1s?

Back

Z = (10.1 - 10.5) / 0.4 = -1.0.

Front

What is the probability of a value being less than the mean in a normal distribution?

Back

The probability of a value being less than the mean is also 0.5 or 50%.