Limited access

Upgrade to access all content for this subject

Most quantitative characters follow a normal distribution as illustrated in the figure below.

Image courtesy of A.D. Herring. Created for Albert.io. Copyright 2016. All rights reserved.

Additionally, the table below for a standardized normal distribution (referred to as the z-distribution) provides the areas in one tail of the distribution relative to the number of standard deviations away from the mean. A z-value of 1.00 indicates that 0.1587 (or 15.9%) of the population is expected to be in the tail of the distribution. This is rounded off to 16%, and therefore, if 16% of the distribution is in each tail, 68% of the distribution is within one standard deviation of the mean.

A z-value is calculated by dividing some quantity by the appropriate standard deviation (this 'standardizes' any distribution relative to the size of the standard deviation for a specific population).

To use the z-value table below, (1) go down the left-most column corresponding to the first decimal place of the z-value to find the correct row, and then (2) go across that row to the column corresponding to the second decimal place of the z-value. For example, the area in the distribution tail corresponding to a z-value of 0.38 is 0.3520.

z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 0.5000 0.4960 0.4920 0.4880 0.4841 0.4801 0.4761 0.4721 0.4681 0.4641
0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4403 0.4364 0.4325 0.4286 0.4247
0.2 0.4207 0.4168 0.4129 0.4091 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
0.6 0.2743 0.2709 0.2676 0.2644 0.2611 0.2579 0.2546 0.2514 0.2483 0.2451
0.7 0.2420 0.2389 0.2358 0.2327 0.2297 0.2266 0.2236 0.2207 0.2177 0.2148
0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
1.0 0.1587 0.1563 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
1.2 0.1151 0.1131 0.1112 0.1094 0.1075 0.1057 0.1038 0.1020 0.1003 0.0985
1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0722 0.0708 0.0694 0.0681
1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
1.8 0.0359 0.0352 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
2.2 0.0139 0.0136 0.0132 0.0129 0.0126 0.0122 0.0119 0.0116 0.0113 0.0110
2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
2.4 0.0082 0.0080 0.0078 0.0076 0.0073 0.0071 0.0070 0.0068 0.0066 0.0064
2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
2.6 0.0047 0.0045 0.0044 0.0043 0.0042 0.0040 0.0039 0.0038 0.0037 0.0036
2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
3.0 0.0014 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010

$\ $
Assume that mature weight (adjusted for sex) in a population of whitetail deer is normally distributed with a mean of 160 lb and a standard deviation of 15 lb.

Select an assignment template