The Normal Distribution Practice

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

What does it mean if a distribution is normal?

Back

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

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

How do you find the z-score for a given value in a normal distribution?

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 is the significance of the z-score in a normal distribution?

Back

The z-score indicates how many standard deviations a value is from the mean, helping to determine the probability of a value occurring.

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

How do you calculate the probability of a value falling below a certain z-score?

Back

You can use the standard normal distribution table (z-table) to find the probability corresponding to a given z-score.