Suppose X is a normally distributed random variable with mean μ and standard deviation σ and that we want to find the following probability
P(a ≤ X ≤ b)
for some interval (a,b). One approach would be for change variables, Z = (X- μ)/σ, and use a lookup table containing values of the cumulative distribution funtion (CDF) for the standard normal random variable Z.
Alternatively, we could just ask a calculator! To use the normal distribution calculator below, give it the lower bound, a, the upper bound, b, then, enter the mean and standard deviation.
For negative infinity enter -1E99, for positive infinity enter 1E99. Note that if you are using z-scores for the lower and upper bounds, make sure you enter a mean of 0, and a standard deviation of 1.
Sometimes, we are given a probability and asked to find the observation that will yield such a result, that is, we want to find c when
P(X ≤ c) = p or P(X ≥ c) = p
for some specified probability p. Once again, we could change variables and use a lookup table, but it can be must faster to use an inverse CDF calculator.
To use the inverse normal distribution calculator below enter the area under the curve (the probability), then, enter the mean and standard deviation. Finally, indicate whether you are inputting a left-
or right-tail probability.
