Normal Distribution Calculator
Evaluate a value under a normal distribution with a chosen mean and standard deviation.
Z-score1
P(X ≤ x)0.841345
P(X > x)0.158655
Density f(x)0.241971
How this tool works
The z-score standardizes x, then the standard normal CDF gives P(X≤x). The normal PDF gives the probability density at x.
Example
For the standard normal distribution, x=1 has cumulative probability about 0.8413.
Common questions
Is the density f(x) itself a probability?
No. For a continuous variable, probability comes from area under the density curve over an interval.
What does the CDF report?
It reports the probability that a normally distributed random variable is less than or equal to x.