# Wolfram Mathematica

## Distribution with Quantity Parameters

Approximate height distribution with normal distribution with mean of 70 inches and standard deviation of 6.5 inches. The distribution can be constructed using Quantity as a corresponding mean and standard deviation parameters and will yield an appropriate QuantityDistribution.

In:= ```height\[ScriptCapitalD] = NormalDistribution[Quantity[70, "Inches"], Quantity[6.5, "Inches"]]```
Out= The distribution represents a random variable in the specified units.

In:= `averageHeight = Mean[height\[ScriptCapitalD]]`
Out= Compute with the distribution using appropriate quantity arguments.

In:= `CDF[height\[ScriptCapitalD], Quantity[170, "Centimeters"]]`
Out= Compute probability that a person's height is between 65 and 72 inches.

In:= ```Probability[Quantity[65, "in"] < x < Quantity[72, "in"], x \[Distributed] height\[ScriptCapitalD]]```
Out= Assuming this height distribution, find an average time of a hat falling from a person's head on Earth.

In:= ```NExpectation[Sqrt[(2 h)/Entity["Planet", "Earth"]["Gravity"]], h \[Distributed] height\[ScriptCapitalD]]```
Out= 