Math2.org Math Tables: z-distribution

(Math)

z-distribution

The z- is a N(0, 1) distribution, given by the equation:

\[ f(z) = \frac{1}{2 \pi} e<sup>{2}</sup> \]

The area within an interval (a,b) = normalcdf(a,b) = \[ \int_a^b e<sup>{2}</sup> \, dz \] (It is not integrable algebraically.)

The Taylor expansion of the above assists in speeding up the calculation:
\[ normalcdf(-\infty,z) = \frac{1}{2} + \frac{1}{\sqrt{2 \pi}} \sum<sub>k=0</sub><sup>\infty</sup> \frac{(-1)^k x<sup>2k+1</sup>}{(2k+1)2^k k!} \]
Standard Normal Probabilities:
(The table is based on the area P under the standard normal probability curve, below the respective z-statistic.)
z.00.01.02.03.04.05.06.07.08.09
-4.00.000030.000030.000030.000030.000030.000030.000020.000020.000020.00002
-3.90.000050.000050.000040.000040.000040.000040.000040.000040.000030.00003
-3.80.000070.000070.000070.000060.000060.000060.000060.000050.000050.00005
-3.70.000110.000100.000100.000100.000090.000090.000080.000080.000080.00008
-3.60.000160.000150.000150.000140.000140.000130.000130.000120.000120.00011
-3.50.000230.000220.000220.000210.000200.000190.000190.000180.000170.00017
-3.40.000340.000320.000310.000300.000290.000280.000270.000260.000250.00024
-3.30.000480.000470.000450.000430.000420.000400.000390.000380.000360.00035
-3.20.000690.000660.000640.000620.000600.000580.000560.000540.000520.00050
-3.10.000970.000940.000900.000870.000840.000820.000790.000760.000740.00071
-3.00.001350.001310.001260.001220.001180.001140.001110.001070.001030.00100
-2.90.001870.001810.001750.001690.001640.001590.001540.001490.001440.00139
-2.80.002560.002480.002400.002330.002260.002190.002120.002050.001990.00193
-2.70.003470.003360.003260.003170.003070.002980.002890.002800.002720.00264
-2.60.004660.004530.004400.004270.004150.004020.003910.003790.003680.00357
-2.50.006210.006040.005870.005700.005540.005390.005230.005080.004940.00480
-2.40.008200.007980.007760.007550.007340.007140.006950.006760.006570.00639
-2.30.010720.010440.010170.009900.009640.009390.009140.008890.008660.00842
-2.20.013900.013550.013210.012870.012550.012220.011910.011600.011300.01101
-2.10.017860.017430.017000.016590.016180.015780.015390.015000.014630.01426
-2.00.022750.022220.021690.021180.020670.020180.019700.019230.018760.01831
-1.90.028720.028070.027430.026800.026190.025590.025000.024420.023850.02330
-1.80.035930.035150.034380.033620.032880.032160.031440.030740.030050.02938
-1.70.044560.043630.042720.041810.040930.040060.039200.038360.037540.03673
-1.60.054800.053700.052620.051550.050500.049470.048460.047460.046480.04551
-1.50.066810.065520.064250.063010.061780.060570.059380.058210.057050.05592
-1.40.080760.079270.077800.076360.074930.073530.072140.070780.069440.06811
-1.30.096800.095100.093420.091760.090120.088510.086910.085340.083790.08226
-1.20.115070.113140.111230.109350.107490.105650.103830.102040.100270.09852
-1.10.135660.133500.131360.129240.127140.125070.123020.121000.119000.11702
-1.00.158650.156250.153860.151500.149170.146860.144570.142310.140070.13786
-0.90.184060.181410.178780.176180.173610.171050.168530.166020.163540.16109
-0.80.211850.208970.206110.203270.200450.197660.194890.192150.189430.18673
-0.70.241960.238850.235760.232690.229650.226630.223630.220650.217690.21476
-0.60.274250.270930.267630.264340.261080.257840.254620.251430.248250.24509
-0.50.308530.305020.301530.298050.294600.291160.287740.284340.280950.27759
-0.40.344570.340900.337240.333590.329970.326350.322760.319170.315610.31206
-0.30.382090.378280.374480.370700.366920.363170.359420.355690.351970.34826
-0.20.420740.416830.412930.409040.405160.401290.397430.393580.389740.38590
-0.10.460170.456200.452240.448280.444330.440380.436440.432500.428570.42465
-0.00.500000.496010.492020.488030.484040.480060.476070.472090.468110.46414

Java Normal Probability Calculator (required JavaScript)
To find the area P under the normal probability curve N(mean, standard_deviation) within the interval (left, right), type in the 4 parameters and press "Calculate". The standard normal curve N(0,1) has a mean=0 and s.d.=1. Use -inf and +inf for infinite limits.

left boundright boundmeanstandard deviation
normal graph