If x is normally distrubed with u = 20.0 and o = 4.0, determine the following:

a. P(x > 20.0)

b. P(16.0 < x < 24.0)

c. P(X < 12)

d. P(x = 22.0)

e. P(12.0 , x , 28.0)

f. P(x 15)

Let y = (x – u) / o = (x – 20) / 4, then x = 4y + 20 and y satisfies the normal distribution.

a. P(x > 20) = P(4y + 20 > 20) = P(y > 0) = 0.5

b. P(16.0 < x < …

This solutions contains explanations and calculations to derive probabilities from a normal distribution.