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If you have a problem with a sample distribution with a given mean and standard deviation, and sample size, use this calculator. This calculates the sampling distribution of the mean using a Standard Normal Distribution.

The formula is denoted below

Z = | X - μ |

σ/n |

This calculator solves for P(x < a), P(x >a), or P(z < x < b). For problems like P(z < x < b), enter the 2 X values with a comma separator, i.e., 250,300.

EXAMPLE: A casino is set to pay out in the form of a random variable with a mean of 200 tokens and a standard deviation of 15 tokens. What is the probability that the average (mean) amount of tokens dispensed in a random sample size of 36 casino players is at least 204 tokens?

Enter 204 for X, 200 for mu(mean), 15 for standard deviation, and 36 for n. Press P(Z >= z). Your answer is 0.0548.