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 8 X 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 pe...

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

Question:

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 = 1.8 X + 32).

a. If the median of the X distribution is µ̃, show that 1.8 µ̃ + 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?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...