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Probability Density

  1. Aug 28, 2010 #1
    1. The problem statement, all variables and given/known data

    c. The life of a certain brand of battery is normally distributed with a mean of 4 years and a
    standard deviation of 1. 2 years.
    i. If a battery is selected at random, what is the probability that it will last for more than 6
    years? (5 marks)
    ii. How long a warranty period should the manufacturer provide if he is willing to replace
    at most 5% of all the batteries sold? (5 marks)

    2. Relevant equations



    3. The attempt at a solution
    Part (i) i can do. Part (ii) dun understand. 5% of all batteries sold? how many are they?
     
  2. jcsd
  3. Aug 28, 2010 #2

    lanedance

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    so a single battery hsould have a 95% probabilty of lasting the warranty period
     
  4. Aug 28, 2010 #3
    24fdaid.jpg


    So should we do (b - a) in years ?
     
  5. Aug 28, 2010 #4

    lanedance

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    i would look at the cumulative distribution & pick of the time at 5%

    as your pdf is defined in years, I would find the answer in years
     
  6. Aug 28, 2010 #5
    I am using this table here
    http://www.intmath.com/Counting-probability/z-table.php

    Could you show me the working.

    Formulae: Z = (X-mean)/standard deviation

    Mean is 4 and standard deviation is 1.2.
    The answer in my test paper shows 2 years
     
  7. Aug 28, 2010 #6
    I tried working from the answer, the Z value have to be -1.65
     
  8. Aug 28, 2010 #7

    lanedance

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    ok so in that table you want to find when the probabilty is 0.45 (the othe side of the curve will give you 0.5 probabiliy as it is symmetric)

    so reading off P = 0.45, at z=1.65

    so 95% of the batteries will have a life greater than
    = Mean - 1.65 x SD
    = 4yrs - 1.65x1.2 = 4-2.3 = 1.7

    which is pretty close to 2
     
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