z score table to standard normal distribution

One of the things that you need to know about the z score table is that this table shows the percentage of values using, in most cases, a decimal figure). Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the The z-scores are –3 and +3 for 32 and 68, respectively. The values 50 – 18 = 32 and 50 + 18 = 68 are within three standard deviations of the mean 50.

About 99.7% of the x values lie within three standard deviations of the mean.

The z-scores are –2 and +2 for 38 and 62, respectively. The values 50 – 12 = 38 and 50 + 12 = 62 are within two standard deviations from the mean 50.

About 95% of the x values lie within two standard deviations of the mean.

The z-scores are –1 and +1 for 44 and 56, respectively. The values 50 – 6 = 44 and 50 + 6 = 56 are within one standard deviation from the mean 50. Therefore, about 68% of the x values lie between –1 σ = (–1)(6) = –6 and 1 σ = (1)(6) = 6 of the mean 50.

About 68% of the x values lie within one standard deviation of the mean.

Suppose x has a normal distribution with mean 50 and standard deviation 6.

The empirical rule is also known as the 68-95-99.7 rule.

The z-scores for +3 σ and –3 σ are +3 and –3 respectively.

The z-scores for +2 σ and –2 σ are +2 and –2, respectively.

The z-scores for +1 σ and –1 σ are +1 and –1, respectively.

Notice that almost all the x values lie within three standard deviations of the mean.

About 99.7% of the x values lie between –3 σ and +3 σ of the mean µ (within three standard deviations of the mean).

About 95% of the x values lie between –2 σ and +2 σ of the mean µ (within two standard deviations of the mean).About 68% of the x values lie between –1 σ and +1 σ of the mean µ (within one standard deviation of the mean).The Empirical RuleIf X is a random variable and has a normal distribution with mean µ and standard deviation σ, then the Empirical Rule states the following: This score tells you that x = 10 is _ standard deviations to the _(right or left) of the mean_(What is the mean?). Suppose Jerome scores ten points in a game. Jerome averages 16 points a game with a standard deviation of four points.

Z score table to standard normal distribution