standard normal probability question

[Rebel*and*Saint]

Standard normal probability distribution equation:

f(z)= 1/square root 2pi * e^-z^2/2

1. What happens as x goes to infin., what happens when x goes to - infin?

2. compute f' (z) and find critical points

3. Determine if critical points are maxima or minima

4. Determine the intervals for which the function is concave up and concave down, and specify for what values of z does the function have inflection points.

 

[galactus]

You do know this is the integral for the famous standard normal graph?.

The inflection points occur at the first standard deviation.

For the inflection points, find the second derivative of \(\displaystyle e^{\frac{-t^{2}}{2}}\)

Set it to 0 and solve for t. If you're familiar with the graph, you should anticipate the solution.

As for the limit, \(\displaystyle \L\\\lim_{x\to\infty}e^{\frac{-t^{2}}{2}}=?\)

You've seen the graph. What does the graph do as x gets large?. Once you get to about 3.5 it gets very close to the x-axis, doesn't it?.... though, it never actually touches it.

Have you ever looked at the standard normal table(z-table)?. This is where they get all those solutions, except they use the integral of said function. It is not evaluated with elementary means.