Answer: Let X be the temperature in °C at which a certain

Chapter 4, Problem 25E

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QUESTION:

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. 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?

Questions & Answers

QUESTION:

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. 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?

ANSWER:

Problem 25E

Answer:

Step1:

We have X be temperature in 0C at which certain chemical reaction takes place, and let Y be the temperature in  0F(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,

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