FAD1015 Statistical Tables (Murdoch & Barnes, 4th Edition)

Quick reference tables for FAD1015 - Mathematics III comprehensive drill and exams.

Table 3: Areas in Upper Tail of the Normal Distribution

$P(Z > z)$ — Probability that a standard normal variable exceeds $z$

$z$ 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641
0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247
0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859
0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483
0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121
0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776
0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451
0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148
0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867
0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611
1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379
1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170
1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985
1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823
1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681
1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559
1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455
1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367
1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294
1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233
2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183
2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143
2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110
2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084
2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048
2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036
2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026
2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019
2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
3.0 .00135

How to use: For $P(Z < z)$ (cumulative probability), use $1 - P(Z > z)$. For $P(Z < -z)$, use $P(Z > z)$ by symmetry.

Table 4: Percentage Points of the Normal Distribution

$P(Z > z_p) = p$ $z_p$
0.50 0.0000
0.45 0.1257
0.40 0.2533
0.35 0.3853
0.30 0.5244
0.25 0.6745
0.20 0.8416
0.15 1.0364
0.10 1.2816
0.05 1.6449
0.025 1.9600
0.01 2.3263
0.005 2.5758
0.001 3.0902
0.0005 3.2905

Table 7: Percentage Points of the t-Distribution

$df$ $t_{0.10}$ $t_{0.05}$ $t_{0.025}$ $t_{0.01}$ $t_{0.005}$
1 3.078 6.314 12.706 31.821 63.657
2 1.886 2.920 4.303 6.965 9.925
3 1.638 2.353 3.182 4.541 5.841
4 1.533 2.132 2.776 3.747 4.604
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
13 1.350 1.771 2.160 2.650 3.012
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
22 1.321 1.717 2.074 2.508 2.819
23 1.319 1.714 2.069 2.500 2.807
24 1.318 1.711 2.064 2.492 2.797
25 1.316 1.708 2.060 2.485 2.787
26 1.315 1.706 2.056 2.479 2.779
27 1.314 1.703 2.052 2.473 2.771
28 1.313 1.701 2.048 2.467 2.763
29 1.311 1.699 2.045 2.462 2.756
30 1.310 1.697 2.042 2.457 2.750
40 1.303 1.684 2.021 2.423 2.704
60 1.296 1.671 2.000 2.390 2.660
120 1.289 1.658 1.980 2.358 2.617
$\infty$ 1.282 1.645 1.960 2.326 2.576

Common values for 95% CI: $t_{0.025} \approx 1.96$ for large $n$ ($> 30$)

Table 1: Cumulative Binomial Probabilities (Partial)

Probability of $r$ or more successes in $n$ trials: $P(X \geq r)$

$n = 5$

$r$ \ $p$ 0.01 0.05 0.10 0.20 0.30 0.40 0.50
0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1 .0490 .2262 .4095 .6723 .8319 .9222 .9688
2 .0010 .0226 .0815 .2627 .4718 .6630 .8125
3 — .0012 .0086 .0579 .1631 .3174 .5000
4 — .0001 .0005 .0067 .0308 .0870 .1875
5 — — — .0003 .0024 .0102 .0313

$n = 10$

$r$ \ $p$ 0.10 0.20 0.30 0.40 0.50
0 1.0000 1.0000 1.0000 1.0000 1.0000
1 .6513 .8926 .9718 .9940 .9990
2 .2639 .6242 .8507 .9536 .9893
3 .0702 .3222 .6172 .8327 .9453
4 .0128 .1209 .3504 .6177 .8281
5 .0016 .0328 .1503 .3669 .6230
6 .0001 .0064 .0473 .1662 .3770

Table 2: Cumulative Poisson Probabilities (Partial)

$P(X \geq r)$ where $\mu =$ mean

$r$ $\mu = 0.5$ $\mu = 1.0$ $\mu = 1.5$ $\mu = 2.0$ $\mu = 2.5$ $\mu = 3.0$ $\mu = 3.5$ $\mu = 4.0$ $\mu = 5.0$
0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1 .3935 .6321 .7769 .8647 .9179 .9502 .9698 .9817 .9933
2 .0902 .2642 .4422 .5940 .7127 .8009 .8641 .9084 .9596
3 .0144 .0803 .1912 .3233 .4562 .5768 .6792 .7619 .8753
4 .0018 .0190 .0656 .1429 .2424 .3528 .4634 .5665 .7350
5 .0002 .0037 .0186 .0527 .1088 .1847 .2746 .3712 .5595
6 — .0006 .0045 .0166 .0420 .0839 .1424 .2149 .3840
7 — .0001 .0009 .0045 .0142 .0335 .0653 .1107 .2378

Quick Reference: Confidence Intervals

Parameter Formula Key Value
Mean ($\sigma$ known) $\bar{x} \pm z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$ $z_{0.025} = 1.96$
Mean ($\sigma$ unknown) $\bar{x} \pm t_{\alpha/2, n-1} \cdot \frac{s}{\sqrt{n}}$ Use t-table
Proportion $\hat{p} \pm z_{\alpha/2} \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ $z_{0.025} = 1.96$

Quick Reference: Hypothesis Testing

Test Test Statistic Rejection Region (two-tailed)
One mean, $\sigma$ known $z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}$ $|z| > z_{\alpha/2}$
One mean, $\sigma$ unknown $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$ $|t| > t_{\alpha/2, n-1}$
One proportion $z = \frac{\hat{p} - p_0}{\sqrt{p_0(1-p_0)/n}}$ $|z| > z_{\alpha/2}$

Related

Source: Murdoch, J. and Barnes, J.A. (1998). Statistical Tables, 4th Edition. Macmillan Press.