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Normal distribution and probability

  1. May 16, 2010 #1
    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. jcsd
  3. May 16, 2010 #2
    Well, the value is exactly:

    [tex] \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{-25} e^{-\frac{x^2}{2}} dx [/tex]

    Using software I get:

    >>> from scipy.stats import norm
    >>> norm.cdf(-25)
    3.056696706382561e-138
     
    Last edited: May 16, 2010
  4. May 16, 2010 #3
    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
     
  5. May 16, 2010 #4
    Oh, I forgot the [itex] \frac{1}{\sqrt{2\pi}} [/itex]. Edited now.
     
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