Let X be the temperature in °C at which a certain chemical reaction takes place, and let...

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 X + 32)is the median of the Y distribution.

b. How is the 90th percentile of the Y distribution related to the 90th 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?