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    Normal Distribution Probability Calculator Tool


Compute normal distribution probabilities using the form below. Please type the population mean and population standard deviation, and provide details about the event you want to compute the probability for (for the standard normal distribution, the mean is 0 and the standard deviation is 1):


Population Mean (μ) =   

Population St. Dev. (σ) =   

Two-Tailed:    ≤ X ≤

Left-Tailed:    X ≤

Right-Tailed:    X ≥



More about the normal distribution probability: The normal probability is a type of continuous probability distribution that can take random values on the whole real line. The main properties of the normal distribution are:
  • It is continuous (and as a consequence, the probability of getting any single, specific outcome is zero)

  • It is "bell shaped" (and that is where the "Bell-Curve" name comes along)

  • It is determined by two parameters: the population mean and population standard deviation

  • It is symmetric with respect to its mean


Using the above normal distribution curve calculator above, we are able to compute probabilities of the form Pr(a ≤ X ≤ b), along with its respective normal distribution graphs. This not exactly a normal probablity density calculator, but it is a normal distribution (cummulative) calculator. Change the parameters for a and b to graph normal distribution based on your calculation needs. If you need to compute Pr(3 ≤ X ≤ 4), you will type "3" and "4" in the corresponding boxes of the script.

One very important special case consists of the case of the standard normal distribution, which corresponds to the case of a normal distribution with mean equal to μ = 0, and standard deviation equal to σ = 1. The cases of a regular normal distribution or of a standard normal distribution can all be handled with the above probability calculator.

 
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