Suppose the random variable X is normally distributed with mean and standard deviation . If Y is a linear function of X -that is,

Suppose the random variable X is normally distributed with mean μ and standard deviation σ. If Y is a linear function of X -that is, Y = a + bX, where a and b are constants-then V is also normally distributed with
Mean = a + bμ
sd = |b|σ
For instance, if X is distributed as N(25, 2) and Y = 7 - 3X, then the distribution of Y is normal with Mean = 7 - 3(25) = -68 and sd = |-3| × 2 = 6.
(a) At the "low" setting of a water heater, the temperature X of water is normally distributed with Mean = 102°F and sd = 4°F. If Y refers to the temperature measurement in the centigrade scale, that is, Y = |(X - 32), what is the distribution of Y?
(b) Referring to part (a), find the probability of [35 < Y < 42].