The Normal Distribution Practice

Front

What is the mean in a normal distribution?

Back

The mean is the average value of a set of data points, representing the center of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion in a set of values.

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 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 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.

Front

How do you find the z-score 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 a z-table used for?

Back

A z-table is used to find the probability that a statistic is below, above, or between certain values in a standard normal distribution.

Front

How do you determine the minimum height in the top 16% of a normal distribution?

Back

To find the minimum height in the top 16%, you can use the z-score corresponding to 0.84 (since 1 - 0.16 = 0.84) and apply the formula: X = μ + zσ.

Front

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

Back

The area under the curve represents the total probability of all outcomes, which equals 1.

Front

How do you calculate the expected number of occurrences in a normal distribution?

Back

To calculate the expected number of occurrences, multiply the total number of observations by the probability of the event.