Normal Distribution Practice

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 empirical rule (68-95-99.7 rule)?

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

How do you calculate the z-score?

Back

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the data point is above the mean, while a negative z-score indicates it is below the mean.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a distribution and is the center point of a normal 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 bell curve.

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. Specific areas correspond to probabilities of certain ranges of values.

Front

How do you find the probability of a value in a normal distribution?

Back

To find the probability of a value, calculate the z-score and then use the standard normal distribution table to find the corresponding probability.

Front

What is the relationship between the mean and median in a normal distribution?

Back

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

Front

What is a percentile in statistics?

Back

A percentile is a measure used to indicate the value below which a given percentage of observations fall. For example, the 50th percentile is the median.