Question: 25. Let X be the temperature in C at which a certain chemical reaction takes place, and let Y be the temperature in F (so

25. 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 , show that 1.8 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?

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