# Normal distribution and probability

1. May 16, 2010

### kliker

1. The problem statement, all variables and given/known data
The time until the first failure occurred in supplies ink to a particular printer brand, follows a normal distribution with μ=1500 and standard deviation(σ) 20 hours of operation. What percentage of these printers will be damaged before the end of 1000 hours of operation

2. Relevant equations

Z = (X - μ)/σ

3. The attempt at a solution

Ok first of all i found the z score, which is (1000-1500)/20 = -25

this gives me 0 percentage, actually i have the table in front of me and it gives values for minimum z = -3 or something

so, is there anything i can do to find the exact result?

2. May 16, 2010

### hgfalling

Well, the value is exactly:

$$\frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{-25} e^{-\frac{x^2}{2}} dx$$

Using software I get:

>>> from scipy.stats import norm
>>> norm.cdf(-25)
3.056696706382561e-138

Last edited: May 16, 2010
3. May 16, 2010

### kliker

where did you get this integral from?

it gives me ouput 0, which is the correct asnwer, I guess

edit:

ok i get it now, you integrated the probability density function

thanks

4. May 16, 2010

### hgfalling

Oh, I forgot the $\frac{1}{\sqrt{2\pi}}$. Edited now.