Normal Distributions

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where most of the observations cluster around the central peak (mean), and probabilities for values further away from the mean taper off equally in both directions.

Front

What are the key parameters of a normal distribution?

Back

The key parameters of a normal distribution are the mean (μ), which indicates the center of the distribution, and the standard deviation (σ), which measures the spread or dispersion of the distribution.

Front

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

Back

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

Front

How do you calculate a score that lies a certain number of standard deviations from the mean?

Back

To calculate a score that lies 'z' standard deviations from the mean, use the formula: Score = Mean + (z * Standard Deviation).

Front

What percent of a normal distribution lies within ±1 standard deviation from the mean?

Back

Approximately 68% of a normal distribution lies within ±1 standard deviation from the mean.

Front

What percent of a normal distribution lies outside of ±2 standard deviations?

Back

Approximately 5% of a normal distribution lies outside of ±2 standard deviations.

Front

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

Back

The standard deviation indicates how spread out the values are around the mean; a smaller standard deviation means the values are closer to the mean, while a larger standard deviation indicates more spread.

Front

If a dataset has a mean of 75 and a standard deviation of 15, what score is at -2 standard deviations?

Back

The score at -2 standard deviations is 45 (75 - 2*15).

Front

In a normal distribution, what is the probability of a value falling between the mean and one standard deviation above the mean?

Back

The probability of a value falling between the mean and one standard deviation above the mean is approximately 34%.

Front

How do you find the area under the normal curve for a specific range?

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To find the area under the normal curve for a specific range, you can use the z-score formula to convert the values to standard scores and then refer to the standard normal distribution table.