I am trying to answer the following: Let X be a continuous random variable with normal distribution with parameters μ = 3 and σ = .2. Find x so that the following holds.
P(X > x) = 2.5%
I tried subtracting each side by μ and dividing each side by σ. I got P(Z > z) = 2.5%, but I am not sure what to do now.
What you are in effect doing here is solving for $k$ in the integral $$\int_k^\infty \frac{5}{\sqrt{2\pi}}\exp\left({-\frac{25}{2}}(x-3)^2\right)dx=0.025$$ or after standardizing the distribution, $$\int_k^\infty\frac{1}{\sqrt{2\pi}}\exp\left({-\frac{z^2}{2}}\right)dz=0.025$$ The value for $k$ that satisfies the integral is approximately $1.96$.