how to find z score standard normal distribution table

Here X is the unscaled data value, μ is the population mean, σ is the population standard deviation, and Z is the corresponding scaled value. If you have a set of normally distributed data with a different mean and standard distribution, you can transform it into standard form with the scaling equation (X-μ)/σ = Z. Z-score tables are based on a normal distribution that has a mean of 0 and a standard deviation of 1. Many variable traits in nature are distributed normally, for instance, human height, shoe size, and scores on certain kinds of intelligence tests. In statistics, the Gaussian or Normal Distribution is one of the most frequently encountered probability density functions. This is demonstrated below:įrom the table, we can observe that p(z=0.80) = 0.7881 and p(z=-1.2) = 0.How to Read a Z-Score Table to Compute Probability We are required to calculate the probability of z being between -1.2 and 0.80. We can also interpret this as – there is a 97.72% probability that the dividends paid by the company will be below $14.

This means that 97.72% of observations lie below a z-score of 2 (2 standard deviations).

Look for a z-score in the first column, and note the corresponding F(Z) value. We can look up the z-score of 2 in the above table. If the company pays a dividend of $14 this year, its z-score is 2 indicating that the current dividends are 2 standard deviations above the mean. The dividends paid by a company every year are normally distributed with a mean of $10 and a standard deviation of $2. In the above table, F(Z) is the probability that a variable from a standard normal distribution will be less than or equal to Z. The following z-table shows the probabilities for z values ranging between – 3 and 3. The standard normal table shows the area (as a proportion, which can be translated into a percentage) under the standard normal curve corresponding to any Z-score or its fraction, i.e., the probability of observing a z-value that is less than the given value. Once we have the z-scores, we can use the standard normal table to calculate the probabilities.

How to find z score standard normal distribution table