The normal CDF calculator determines the area under the normal distribution curve based on the specified lower and upper bounds, mean, and standard deviation.
The normal cumulative distribution function (CDF) computes the probability that a random variable follows a normal distribution that is less than or equal to a given value.
Let's take an example to understand how normal CDF is calculated.
Find the probability for a normally distributed variable with a mean of 85 and a standard deviation of 20 falls between 98 and 117.
Here,
Lower bound (a) = 98,
Upper bound (b) = 117,
Mean (μ) = 85,
Standard Deviation (σ) = 20.
1. Standardize the Bounds
First, convert the lower and upper bounds into the standard normal distribution using the Zscore formula.
Z_{a} = 

= 

= 0.65 
Z_{b} = 

= 

= 1.6 
2. Find the Probabilities
Now find the probabilities for the Zscores (Z_{a} and Z_{b}) using the standard normal distribution table or calculator.
P(Z_{a}) ≈ 0.74215389
P(Z_{b}) ≈ 0.94520071
3. Calculate the Area (probability)
To compute the area, find the difference between the probability values.
P(a ≤ X ≤ b) = P(Z_{b})  P(Z_{a})
= 0.94520071  0.74215389
= 0.20304682
So, the probability P(98 ≤ X ≤ 117) is 0.203047 or 20.30%.