8.2 Normal Distribution

Front

What is the mean (μ) in a normal distribution?

Back

The mean (μ) is the average value of a set of data points in a normal distribution, representing the center of the distribution.

Front

What is the standard deviation (σ) in a normal distribution?

Back

The standard deviation (σ) measures the dispersion or spread of data points around the mean in a normal distribution.

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 of -2.5 indicate?

Back

A z-score of -2.5 indicates that the data value is 2.5 standard deviations below 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 (μ ± σ) 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 (μ ± 2σ) 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 (μ ± 3σ) of the mean.

Front

What is the empirical rule in statistics?

Back

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

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the total probability of all outcomes, which equals 1 (or 100%).

Front

How do you find the cutoff for a specific percentile in a normal distribution?

Back

To find the cutoff for a specific percentile, use the z-score corresponding to that percentile and apply the formula: X = μ + zσ.