Let X Be the Temperature In $- C$ At Which a Certain Chemical Reaction Takes Place, and Let

Essay

Let X be the temperature in $- C$ at which a certain chemical reaction takes place, and let Y be the temperature in $- F$ (so Y = 1.8X + 32).
a. If the median of the X distribution is $\mu ^ { 2 }$
, show that 1.8 $\tilde { \mu }$
+ 32 is the median of the Y distribution.
b. How is the 90^th percentile of the Y distribution related to the 90^th percentile of the X distribution? Verify your conjecture.
c. More generally, if Y = aX + b, how is any particular percentile of the Y distribution related to the corresponding percentile of the X distribution?