Normal Distribution Calculator

This finds the area under a normal curve between two values, and the value that sits at a given cumulative probability. Enter a mean, a standard deviation and either a pair of bounds or a probability, and you get the probability, the matching z-scores, both tail areas and the symmetric interval around the mean. The cumulative function is evaluated with Hart's rational approximation and the inverse with Acklam's, refined once against it, so nothing is read off a z-table in hundredths. All of it assumes the data really is normal, which is worth checking before leaning on a tail probability.