A normal random variable x has an unknown mean and standard

A normal random variable x has an unknown mean and standard deviation. The probability that x exceeds 3 is 0.9772, and the probability that x exceeds 4 is 0.9332. Find and .

Solution

P[X > 4 ] = 0.9772
P[X > 5 ] = 0.9332

Let Z be the standard normal
P[Z > -2.00] = 0.9772
P[Z > -1.50] = 0.9332

So this means you have two equations
(4 - ?) / ? = -2.00
(5 - ?) / ? = -1.50

solve the system of equations and
? = 8.
? = 2.