with work The random variable x has a normal distribution wi

*with work*

The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x₀, such that:

P(x > x₀) = .95

Solution

P(x > x₀) = .95

First find z0 such that

P(Z>z0) = 0.95

z0 = 1.645

x0 = Mean + z0 (std dev)

= 50 + 14.805

=64.805