Normal Distribution

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a distribution, 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 of a set of values. In a normal distribution, it determines the width of the curve.

Front

What does the empirical rule state?

Back

The empirical rule states that for a normal distribution, approximately 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

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

Back

68%.

Front

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

Back

95%.

Front

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

Back

99.7%.

Front

If the mean is 12 days and the standard deviation is 3 days, what percent of products last between 12 and 15 days?

Back

34%.

Front

In a normal distribution, what does it mean if a data point is one standard deviation above the mean?

Back

It means that the data point is higher than the average value and falls within the upper 34% of the distribution.

Front

How do you calculate the z-score for a data point?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.