Question

g Suppose that a temperature is represented by the random variable X, whose units are in Rankine, with standard deviation 6 Rankine. Let Y be the equivalent random variable with units converted to degrees Celsius. What is the variance of Y , rounded to one decimal point?

Answer 1

`x` degrees Rankine is about
`\frac59x-(5463)/(20)` degrees Celsius, so that

`Y=\frac59X-(5463)/(20)`

The variance of
`Y` is

`\mathrm{Var}[Y]=\mathrm{Var}\left[\frac59X-(5463)/(20)\right]=(25)/(81)\mathrm{Var}[X]=\frac{100}9\approx\boxed{11.1}`