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

## Problem 25E Chapter 4

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 25E

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.?? f 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 ? ? istribution? Verify your conjecture. c.?? ore 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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Problem 25E Answer: Step1: 0 We have X be temperature in C at which certain chemical reaction takes place, and let Y be the temperature in F(so Y = 1.8X + 32). We need to find, 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 Step2: a). Consider, Y = 1.8X + 32 Let Y = h(x) = 1.8x + 32 Now, E(Y) = E(h(x)) = E(1.8x + 32) = 1.8[E(x) + 32] = 1.8 +32 Therefore, If the median of...

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