Standard Normal Random Variable

Date: 04/19/99 at 11:07:42
From: lorianne lowe
Subject: College statistics 124

I need serious help.

Q: Find each of the following for a standard normal random variable Z.
(a)  P( -0.65<Z<1.70 )
(b)  P( Z > -1.03 )

I need to be shown how to do this in steps.

Date: 04/19/99 at 18:03:33
From: Doctor Pat
Subject: Re: College statistics 124

Lorianne,

I assume you have either a z-table or a calculator that will give you 
the probabilities for each z-score.  

A) Find the probability of Z in an interval  P( -0.65<Z<1.70 )

Step one: find the area left of the lefthand interval limit (that is, 
look up the value under a z-score of -.65 in the table. It should be 
about .258. This means that about 25% of the values are to the left of 
this value (-.65) and about 75% are to the right.) 
  
Step two: find the area to the left of the righthand interval limit 
(1.70). This should be about .955 indicating that 95% of the z-values 
are smaller and about 5% are larger.  

Step three: since we want the probability between these, we subtract 
the area left of -.65 from the area left of 1.70 and get the area 
between them. In your problem, .955-.258 gives about .697 . 

B) To find the probability of Z > -1.03 find the probability that Z is 
less than that by looking up the value in the table; then subtract the 
answer from 1 since the total probability is one.

Hope this helps.

- Doctor Pat, The Math Forum
  http://mathforum.org/dr.math/