Z table in statistics

Question

Question involves converting 4 and 15 to Z table with given standard deviation and average. But now, they ask for percentage of probability of anything less than 4 or greater than 15. What am I looking for here on the Z table?

Answer 1

This depend on what the mean and standard deviation is. Let $\mu$ be the mean $\sigma$ be the standard deviation, then

you calculate $x=\dfrac{5-\mu}{\sigma}$, $y=\dfrac{14-\mu}{\sigma}$

I am going to let $\Phi$ denote the number you look up. Note, this always have to be positive

If $x<0$, for probability smaller than $x$, you need to look at $1-\Phi(-x)$ If $x>0$, for probability smaller than $x$, you need to look at $\Phi(x)$

If $y<0$, for probability greater than $x$, you need to look at $\Phi(y)$ If $y>0$, for probability greater than $x$, you need to look at $1-\Phi(y)$

To see this is true, you need to look at the Gaussian distribution's cumulative density function and notice it is symmetric. This is the table I am talking about:

http://statstutorstl.blogspot.co.uk/2010/07/z-table-gives-probabilty-distribution.html