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## Q. 4.22

A chemist measures the temperature of a solution in °C. The measurement is denoted C and is normally distributed with mean 40°C and standard deviation 1°C. The measurement is converted to op by the equation F = 1.8C + 32. What is the distribution of F?

## Verified Solution

Since C is normally distributed, so is F. Now $μ_{C}$ = 40, so $μ_{F}$ = 1.8(40) + 32 = 104, and $\sigma^{2}_{C}$ = 1, so $\sigma^{2}_{F}$ = 1.8²(1) = 3.24. Therefore F ∼ N(104, 3.24).