**How to Find the Z-Score**

The z-score is a measure of how many standard deviations a data point is away from the mean. It is calculated by subtracting the mean from the data point and then dividing the result by the standard deviation.

The z-score can be used to compare data points from different distributions. For example, you could use the z-score to compare the heights of students in two different classes.

To find the z-score, you will need to know the mean and standard deviation of the distribution. The mean is the average of all the data points. The standard deviation is a measure of how spread out the data is.

Once you have the mean and standard deviation, you can use the following formula to calculate the z-score:

`z = (x - mu) / sigma`

where:

- z is the z-score
- x is the data point
- mu is the mean
- sigma is the standard deviation

For example, let’s say you have a data set with a mean of 100 and a standard deviation of 10. To find the z-score for a data point of 110, you would use the following formula:

`z = (110 - 100) / 10 = 1`

This means that the data point is 1 standard deviation above the mean.

The z-score can be used to answer a variety of questions about data. For example, you could use the z-score to find the percentage of data points that are above or below the mean. You could also use the z-score to find the probability of a data point occurring.

**FAQ**

**What is the difference between a z-score and a t-score?**

A z-score is a measure of how many standard deviations a data point is away from the mean of a normal distribution. A t-score is a measure of how many standard deviations a data point is away from the mean of a t-distribution. The t-distribution is a bell-shaped distribution that is similar to the normal distribution, but it has thicker tails. This means that the t-distribution is more likely to produce extreme values than the normal distribution.

**How do I find the z-score for a data point that is not normally distributed?**

If the data point is not normally distributed, you can use a non-parametric test to calculate the z-score. Non-parametric tests do not make assumptions about the distribution of the data.

**What is the probability of a data point having a z-score of 2?**

The probability of a data point having a z-score of 2 is 0.0228. This means that only 2.28% of data points will have a z-score of 2 or higher.

**How can I use the z-score to make predictions?**

The z-score can be used to make predictions about the future. For example, you could use the z-score to predict the probability of a student passing a test.

**What are some of the limitations of the z-score?**

The z-score is a useful tool for analyzing data, but it has some limitations. For example, the z-score can only be used to compare data points from the same distribution. The z-score is also not robust to outliers. This means that a single outlier can have a significant impact on the z-score.

**Conclusion**

The z-score is a powerful tool for analyzing data. It can be used to compare data points from different distributions, to find the percentage of data points that are above or below the mean, and to find the probability of a data point occurring. However, the z-score has some limitations. It can only be used to compare data points from the same distribution, and it is not robust to outliers.