Chapter 4
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 ºF by the equation F = 1.8C + 32. What is the distribution of F?
Step-by-Step
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} = 1.8^2(1) = 3.24. Therefore F ∼ N(104, 3.24).