CDF PDF Calculator

Must be greater than zero. Enter the standard deviation, not the variance.
Only used by the "between" and "outside" modes.
Used by the inverse mode: the area to the left of the value you want.
Used by the critical-value mode and for the returned confidence interval.
Probability
0.975002
Normal Distribution Calculator
Probability
97.50021 %
Z score of x
1.96
Z score of the upper bound
2.58
Density f(x)
0.058441
P(X < x)
0.975002
P(X > x)
0.024998
P(a < X < b)
0.020058
P(X < a or X > b)
0.979942
Percentile of x
97.50021 %
Inverse: x with the given area to its left
1.959964
Inverse: the corresponding z
1.959964
Two-sided critical z
1.959964
One-sided critical z
1.644854
Within 1 sigma
68.268949 %
Within 2 sigma
95.449974 %
Within 3 sigma
99.73002 %
Variance (sigma squared)
1
Worked out from NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.6.1 Normal Distribution and 2 other sources.

How this is worked out

5 steps
  1. X ~ Normal(mu = 0, sigma = 1), so the variance is 1.
  2. z = (1.96 - 0) / 1 = 1.96
  3. P(X < 1.96) = Phi(1.96) = 0.9750021049
  4. P(X > 1.96) = 1 - Phi(1.96) = 0.0249978951
  5. That places 1.96 at the 97.5002th percentile.
Confidence interval around the meantable
-1.959964, 1.959964
One-sigma intervaltable
-1, 1
Two-sigma intervaltable
-2, 2
Three-sigma intervaltable
-3, 3

Results are general information, not financial, tax, legal, medical or engineering advice.