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Math Help - Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

  1. #1
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    Question Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

    The lifespan of lightbulbs in a photographic machine is normally distributed with a mean of 210 hours and a standard deviation of 50 hours.



    1) Determine the z-score of a light bulb with a lifespan of exactly 124hours.

    z= x-mean/standard deviation

    z= (124-210)/50
    x= -1.72

    Z-Score = -1.72


    2) What is the probability that a randomly chosen light bulb would have a lifespan of less than 180 hours?

    z= x-mean/standard deviation
    z= (180-210)/50
    z= -0.60

    p(x<180) = p(z<-0.60) = 0.2258

    Probability= 0.2258 / 22.58%

    3) What is the probability that a randomly chosen light bulb would have a lifespan of between 200 and 250 hours?

    z= x-mean/standard deviation FOR BOTH 200 and 250:

    For200:
    z= x-mean/standard deviation
    z= (200-210)/50
    z= -0.2

    For250:
    z= x-mean/standard deviation
    z= (250-210)/50
    z= 0.8


    p(200<z<250) = p(-0.2<z<0.8) = p(z<0.8) - p(z<-0.2) = 0.7881 - 0.4207 = 0.3674 **Not sure if those italic/underlined numbers are correct on this line**
    Probability = 0.3674 / 36.74%
    Last edited by tdotodot; April 4th 2013 at 07:39 AM.
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  2. #2
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    Re: Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

    Hey tdotodot.

    1) is correct
    2) is not. Using R we get
    > pnorm(-0.6,0,1)
    [1] 0.2742531
    3) Looks good. Again using R:
    pnorm(0.8,0,1) - pnorm(-0.2,0,1)
    [1] 0.3674043
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  3. #3
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    Re: Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

    Quote Originally Posted by chiro View Post
    Hey tdotodot.

    1) is correct
    2) is not. Using R we get
    > pnorm(-0.6,0,1)
    [1] 0.2742531

    3) Looks good. Again using R:
    pnorm(0.8,0,1) - pnorm(-0.2,0,1)
    [1] 0.3674043
    Thank you, really appreciate your help. Could you tell me how you got 0.2752531 for question #2? And what is "R"?

    I am using the Z-Score chart, row 0.6 / column 0.00 shows the number 0.2258 and column 0.01 shows .2291. Other than that, looks good.
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  4. #4
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    Re: Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

    pnorm(z,0,1) calculates the probability P(Z < z) where Z ~ N(0,1). I used this command to verify your answer.

    R is an open source statistical package that is becoming one of the most popular platforms used in statistics.

    The R Project for Statistical Computing
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