19.5 Normal Distribution 647
TABLE 19.11 Areas Under the Standard Normal Curve—the Values were Generated using the Standard Normal Distribution
Function of Excel (continued)Z AZAZAZAZAZAZA
0.21 0.0832 0.72 0.2642 1.23 0.3907 1.74 0.4591 2.25 0.4878 2.76 0.4971 3.27 0.4995
0.22 0.0871 0.73 0.2673 1.24 0.3925 1.75 0.4599 2.26 0.4881 2.77 0.4972 3.28 0.4995
0.23 0.0910 0.74 0.2704 1.25 0.3944 1.76 0.4608 2.27 0.4884 2.78 0.4973 3.29 0.4995
0.24 0.0948 0.75 0.2734 1.26 0.3962 1.77 0.4616 2.28 0.4887 2.79 0.4974 3.3 0.4995
0.25 0.0987 0.76 0.2764 1.27 0.3980 1.78 0.4625 2.29 0.4890 2.8 0.4974 3.31 0.4995
0.26 0.1026 0.77 0.2794 1.28 0.3997 1.79 0.4633 2.3 0.4893 2.81 0.4975 3.32 0.4995
0.27 0.1064 0.78 0.2823 1.29 0.4015 1.8 0.4641 2.31 0.4896 2.82 0.4976 3.33 0.4996
0.28 0.1103 0.79 0.2852 1.3 0.4032 1.81 0.4649 2.32 0.4898 2.83 0.4977 3.34 0.4996
0.29 0.1141 0.8 0.2881 1.31 0.4049 1.82 0.4656 2.33 0.4901 2.84 0.4977 3.35 0.4996
0.3 0.1179 0.81 0.2910 1.32 0.4066 1.83 0.4664 2.34 0.4904 2.85 0.4978 3.36 0.4996
0.31 0.1217 0.82 0.2939 1.33 0.4082 1.84 0.4671 2.35 0.4906 2.86 0.4979 3.37 0.4996
0.32 0.1255 0.83 0.2967 1.34 0.4099 1.85 0.4678 2.36 0.4909 2.87 0.4979 3.38 0.4996
0.33 0.1293 0.84 0.2995 1.35 0.4115 1.86 0.4686 2.37 0.4911 2.88 0.4980 3.39 0.4997
0.34 0.1331 0.85 0.3023 1.36 0.4131 1.87 0.4693 2.38 0.4913 2.89 0.4981 3.4 0.4997
0.35 0.1368 0.86 0.3051 1.37 0.4147 1.88 0.4699 2.39 0.4916 2.9 0.4981 3.41 0.4997
0.36 0.1406 0.87 0.3078 1.38 0.4162 1.89 0.4706 2.4 0.4918 2.91 0.4982 3.42 0.4997
0.37 0.1443 0.88 0.3106 1.39 0.4177 1.9 0.4713 2.41 0.4920 2.92 0.4982 3.43 0.4997
0.38 0.1480 0.89 0.3133 1.4 0.4192 1.91 0.4719 2.42 0.4922 2.93 0.4983 3.44 0.4997
0.39 0.1517 0.9 0.3159 1.41 0.4207 1.92 0.4726 2.43 0.4925 2.94 0.4984 3.45 0.4997
0.4 0.1554 0.91 0.3186 1.42 0.4222 1.93 0.4732 2.44 0.4927 2.95 0.4984 3.46 0.4997
0.41 0.1591 0.92 0.3212 1.43 0.4236 1.94 0.4738 2.45 0.4929 2.96 0.4985 3.47 0.4997
0.42 0.1628 0.93 0.3238 1.44 0.4251 1.95 0.4744 2.46 0.4931 2.97 0.4985 3.48 0.4997
0.43 0.1664 0.94 0.3264 1.45 0.4265 1.96 0.4750 2.47 0.4932 2.98 0.4986 3.49 0.4998
0.44 0.1700 0.95 0.3289 1.46 0.4279 1.97 0.4756 2.48 0.4934 2.99 0.4986 3.5 0.4998
0.45 0.1736 0.96 0.3315 1.47 0.4292 1.98 0.4761 2.49 0.4936 3 0.4987 3.51 0.4998
0.46 0.1772 0.97 0.3340 1.48 0.4306 1.99 0.4767 2.5 0.4938 3.01 0.4987 3.52 0.4998
0.47 0.1808 0.98 0.3365 1.49 0.4319 2 0.4772 2.51 0.4940 3.02 0.4987 3.53 0.4998
0.48 0.1844 0.99 0.3389 1.5 0.4332 2.01 0.4778 2.52 0.4941 3.03 0.4988 ... ...
0.49 0.1879 1 0.3413 1.51 0.4345 2.02 0.4783 2.53 0.4943 3.04 0.4988 ... ...
0.5 0.1915 1.01 0.3438 1.52 0.4357 2.03 0.4788 2.54 0.4945 3.05 0.4989 3.9 0.5000Example 19.5 Using Table 19.11, show that for a standard normal distribution of a data set, approximately
68% of the data will fall in the interval of stos, about 95% of the data falls between 2 sto
2 s, and approximately all of the data points lie between 3 sto 3s.
In Table 19.11,z1 represents one standard deviation above the mean and 34.13% of
the total area under a standard normal curve. On the other hand,z1 represents one stan-
dard deviation below the mean and 34.13% of the total area, as shown in Figure 19.7. There-
fore, for a standard normal distribution, 68% of the data fall in the interval ofz1 to
z1 (stos). Similarly, z2 and z2 (two standard deviations below and above theCopyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀