Practice with z scores and tables

A Z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: $$Z = \frac{(X - \mu)}{\sigma}$$ where X is the value, $$\mu$$ is the mean, and $$\sigma$$ is the standard deviation.

To find the area to the right of a Z-score, you can use a Z-table or standard normal distribution table. The area to the right is equal to 1 minus the area to the left of the Z-score.

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

A negative Z-score indicates that the value is below the mean of the data set.

A positive Z-score indicates that the value is above the mean of the data set.

To calculate a Z-score, use the formula: $$Z = \frac{(X - \mu)}{\sigma}$$ where X is the value, $$\mu$$ is the mean, and $$\sigma$$ is the standard deviation.

The standard deviation measures the dispersion or spread of a set of values in a normal distribution. It indicates how much the values deviate from the mean.

The area under the normal curve represents the probability of a value falling within a certain range. The total area under the curve is equal to 1.

A Z-score of -2.33 means the value is 2.33 standard deviations below the mean, indicating it is relatively low compared to the average.

The empirical rule states that for a normal distribution: approximately 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.