# Standard normal distribution - the z-table for the PDF

I have searched high and low, and I simply cannot find this table anywhere. I am quite sure that for practical purposes I don't need it - that there are other methods, but it would be extremely useful if anybody could point me in the right direction of finding one online. Also, it needs to have negative values.

I have a funny feeling I'm going to get a ribbing for asking this. Have mercy.

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This is the CDF - I need the PDF, the values along the line, not the area underneath. – SLD Dec 17 '12 at 8:25
Normal tables are made because there is no explicit form of the integral of the normal pdf. If you want the values of the pdf, you can calculate them using the formula $f(x)=\frac{1}{\sqrt{2\pi \sigma^2}}\exp{\{- \frac {(x-\mu)^2}{2 \sigma^2}}\}$. – caburke Dec 17 '12 at 8:37
@SLD if you need the pdf, you need to modify the question to ask for the density rather than the distribution. The distribution is the cdf. But for the pdf, you shouldn't need tables, since you can just evaluate the function. If you use R or Excel you can get the thing for whatever value you need. – Glen_b Dec 17 '12 at 9:23
Thank you for the comments. I apologise for the misuse of language. I understand there are better ways to go about this than the table, however for completely benign reasons I did need the table, and I'm not savvy enough to generate it myself. Thanks for the time you've put in. – SLD Dec 17 '12 at 9:36
Because the PDF at $-z$ is the same as the PDF at $z$, there is no need for tables with negative values. Whence something like this will work fine (out to $5.9$, anyway). – whuber Dec 17 '12 at 16:39

Here is one made specially for you. Note that the density of a distribution symmetric about $0$ is the same for positive and negative values.

          density      cumprob
-3.5 0.0008726827 0.0002326291
-3.4 0.0012322192 0.0003369293
-3.3 0.0017225689 0.0004834241
-3.2 0.0023840882 0.0006871379
-3.1 0.0032668191 0.0009676032
-3   0.0044318484 0.0013498980
-2.9 0.0059525324 0.0018658133
-2.8 0.0079154516 0.0025551303
-2.7 0.0104209348 0.0034669738
-2.6 0.0135829692 0.0046611880
-2.5 0.0175283005 0.0062096653
-2.4 0.0223945303 0.0081975359
-2.3 0.0283270377 0.0107241100
-2.2 0.0354745928 0.0139034475
-2.1 0.0439835960 0.0178644206
-2   0.0539909665 0.0227501319
-1.9 0.0656158148 0.0287165598
-1.8 0.0789501583 0.0359303191
-1.7 0.0940490774 0.0445654628
-1.6 0.1109208347 0.0547992917
-1.5 0.1295175957 0.0668072013
-1.4 0.1497274656 0.0807566592
-1.3 0.1713685920 0.0968004846
-1.2 0.1941860550 0.1150696702
-1.1 0.2178521770 0.1356660609
-1   0.2419707245 0.1586552539
-0.9 0.2660852499 0.1840601253
-0.8 0.2896915528 0.2118553986
-0.7 0.3122539334 0.2419636522
-0.6 0.3332246029 0.2742531178
-0.5 0.3520653268 0.3085375387
-0.4 0.3682701403 0.3445782584
-0.3 0.3813878155 0.3820885778
-0.2 0.3910426940 0.4207402906
-0.1 0.3969525475 0.4601721627
0    0.3989422804 0.5000000000
0.1  0.3969525475 0.5398278373
0.2  0.3910426940 0.5792597094
0.3  0.3813878155 0.6179114222
0.4  0.3682701403 0.6554217416
0.5  0.3520653268 0.6914624613
0.6  0.3332246029 0.7257468822
0.7  0.3122539334 0.7580363478
0.8  0.2896915528 0.7881446014
0.9  0.2660852499 0.8159398747
1    0.2419707245 0.8413447461
1.1  0.2178521770 0.8643339391
1.2  0.1941860550 0.8849303298
1.3  0.1713685920 0.9031995154
1.4  0.1497274656 0.9192433408
1.5  0.1295175957 0.9331927987
1.6  0.1109208347 0.9452007083
1.7  0.0940490774 0.9554345372
1.8  0.0789501583 0.9640696809
1.9  0.0656158148 0.9712834402
2    0.0539909665 0.9772498681
2.1  0.0439835960 0.9821355794
2.2  0.0354745928 0.9860965525
2.3  0.0283270377 0.9892758900
2.4  0.0223945303 0.9918024641
2.5  0.0175283005 0.9937903347
2.6  0.0135829692 0.9953388120
2.7  0.0104209348 0.9965330262
2.8  0.0079154516 0.9974448697
2.9  0.0059525324 0.9981341867
3    0.0044318484 0.9986501020
3.1  0.0032668191 0.9990323968
3.2  0.0023840882 0.9993128621
3.3  0.0017225689 0.9995165759
3.4  0.0012322192 0.9996630707
3.5  0.0008726827 0.9997673709

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One possibily to obtain @Henry's table is the 'dnorm()' function in R ;-) – ocram Dec 17 '12 at 8:42
Thank you for this, I'm very very grateful. – SLD Dec 17 '12 at 9:36
@ocram: indeed these two columns came from dnorm() and pnorm() in R – Henry Dec 17 '12 at 18:40