Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P (0 < z < a) = 0.4608, find a.


Please do not just list the answer because I can find them on the internet, I want to be able to know how to solve this for my exam

thanks!

plug in the values for the mean (0) and variance (1) into the formula for a normal distribution

and you get this:
f(x) = 1/root(2pi) * e^(-x^2/2)

this gives you a nice, normal curve that looks like the red one in this nice wikipedia page:
http://en.wikipedia.org/wiki/File:Normal_Distribution_PDF.svg

P(0 < z < a) is essentially equal to the area under the curve between 0 and a (fun fact: the area from negative infinity to infinity under any probability distribution curve is always 1)

so take the integral of f(x) between 0 and a, and set that to equal 0.4608

solve for a

(I cba to do the actual calculus and plugging in. If you can't do integrals, you should probably drop your class while you're behind.)

This post was edited by irimi on Nov 1 2011 04:46am

lol, i cant tell if your trolling or just being a bit of a git.. there's no way he'd be able to do integrate a normal distribution, if he is asking for help with this ( it requires squaring the integral and then using a polar coordinate subsitution )

Basically, do you have probability tables?

The probability your looking for is P(z<a) - P(z<0)

We know Probability z< 0 = 0.5 ( as the distriubtion is symetric around 0 and the total area under the curve = 1, so half of 1 is 1/2 )

now we have 0.4608 = P(z<a) - 0.5

0.9608 = P(z<a)

only way to do this is to look up " 0.9608" in your tables, and see which value it corresponds to.

Or if you are using computer software, its the qnorm(0.9608)

1.760046 should be the answer for a then