# Chapter 6 - Normal Probability Distributions - 6-2 The Standard Normal Distribution - Beyond the Basics - Page 258: 49

a)68.26% b)2.28% c)95% d)95.44% e)0.13%

#### Work Step by Step

a)Using the table, the probability of z being between -1 and 1 is equal to the probability of z being less than 1 minus the probability of z being less than -1, which is: 0.8413-0.1587=0.6826=68.26%. b)Using the table, the probability of z being more than 2 is equal to 1 minus the probability of z being less than 2, which is: 1-0.9772=0.0228=2.28%. c)Using the table, the probability of z being between -1.96 and 1.96 is equal to the probability of z being less than 1.96 minus the probability of z being less than -1.96, which is: 0.9750-0.0250=0.95=95%. d)Using the table, the probability of z being between -2 and 2 is equal to the probability of z being less than 2 minus the probability of z being less than -2, which is: 0.9772-0.0228=0.9544=95.44%. e)Using the table, the probability of z being more than 3 is equal to 1 minus the probability of z being less than 3, which is: 1-0.9987=0.0013=0.13%.

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