The Normal Distribution Practice

Front

What is the Empirical Rule in statistics?

Back

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

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

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

95% of the data falls within two standard deviations of the mean.

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

99.7% of the data falls within three standard deviations of the mean.

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 is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of the distribution.

Front

If the mean number of accidents is 6.4 and the standard deviation is 1.5, what is the probability of having more than 7 accidents?

Back

The probability of having more than 7 accidents is approximately 0.3446.

Front

In a normal distribution, what is the minimum height in the top 16% if the mean height is 69.6 inches and the standard deviation is 3.0 inches?

Back

The minimum height in the top 16% is 72.6 inches.

Front

What is the mean of a normal distribution?

Back

The mean of a normal distribution is the average of all data points and is the center of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.