Let X be the temperature in C at which a certain chemical

Chapter 4, Problem 4.33

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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? 2

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