# Business application Z-scores

• Jul 14th 2011, 04:11 PM
sfspitfire23
Fellas,

I have monthly cash flows from a business (values are positive and negative, with positive values indicating that the business gained money and vice versa) with a mean of -233698 and a SD of 3026624. I want to calculate the probability of cash flows in any given month being greater than +2000000 and less than -2000000. I'm assuming normality.

So, heres what I'm doing:

For the less than -2000000:
P(X<-2000000)=P(X<(-2000000+233698)/3026624)=-.2531.

Integrating against a standard normal variable with bounds (-infinity to -.2531) I get a probability of .4001.

So, there is a 40% chance in any given month that cash flows will be less than -2000000.

Is this mathematically correct?

(pickslides thank you for helping out before)
• Jul 14th 2011, 05:21 PM
pickslides
Re: Business application Z-scores
Quote:

Originally Posted by sfspitfire23
Fe

For the less than -2000000:
P(X<-2000000)=P(X<(-2000000+233698)/3026624)=-.2531.

You should say
$\displaystyle \displaystyle P(X<-2000000)= P\left(Z< \frac{-2000000-(-233698)}{3026624}\right) = P(Z<-0.58)$ $\displaystyle = 0.28$