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 $\dfrac59x-\dfrac{5463}{20}$ degrees Celsius, so that

$Y=\dfrac59X-\dfrac{5463}{20}$

The variance of $Y$ is

$\mathrm{Var}[Y]=\mathrm{Var}\left[\dfrac59X-\dfrac{5463}{20}\right]=\dfrac{25}{81}\mathrm{Var}[X]=\dfrac{100}9\approx\boxed{11.1}$