z score table for standard normal distribution

Z score = (x – μ) / σ = (700-600) / 150 = 0.68Ģ) Using the Z-score table we can find out how well she performed relative to her peers. Solution1) From the above-given data, we can deduce that: Find out how well Sarah performed compared to her peers. The average score was 500 (µ) and the standard deviation was 120 (σ). Imagine a group of 300 applicants who took a math test.

Then, the intersecting point of the columns and rows provides us with the area under the normal curve or the probability. (The integer part and the first decimal of Z-score are present in the row label).Īcross the topmost row of the table, the part which denotes the z-score denotes the hundredth. In the first column of the table, we can find out the number of standard deviations either above or below the mean value to one decimal place. The mean of these tables is 0 and 1 is their standard deviation. The table given above is designed specifically for standard normal distribution. These tables are specifically designed for a standard normal distribution, which has a mean of 0 and a standard deviation of 1. A Z-Score Table is a table that shows the percentage of values (or area percentage) to the left of a given z-score on a standard normal distribution.Ī positive Z-score means that the observed value is above the mean of total values.Ī negative Z-score value indicates the observed value is below the mean of total values. To find a specific area under a normal curve, first, find the z-score of the data value and then use a Z-Score Table to find the area. This z-score will tell you how many standard errors are there between the sample mean and the population means. Standard Error of the Mean: When you have multiple samples and want to describe the standard deviation of those sample means (the standard error) use this z score formula: Putting the values in the equation mentioned above, Solution From the question above we can deduce that,Īnd the value of standard deviation (σ) is 30 Assuming it is a normal distribution, your z score would be. The test has a mean (μ) of 140 and a standard deviation (σ) of 30. Let's take an example and understand this better. Where x̄ is the sample means is the sample standard deviation. How to Calculate Z-score?įor a sample, the basic z- score formula is When you 'standardize' a variable, its mean becomes zero and its standard deviation becomes one. Z-scores range from -3 standard deviations up to +3 standards.Ī Z-score can help us in determining the difference or the distance between a value and the mean value.

A raw score as a Z-score can also be called a standard score and it can be placed on a normal distribution curve. A data point is a measure of how many standard deviations are below or above the mean. Z-score can be defined as the number of standard deviations from the mean.

Z score table for standard normal distribution