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Math Help - Questions Involving Z-Score, Can you please check my answer?

  1. #1
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    Question Questions Involving Z-Score, Can you please check my answer?

    1. The lifespan of a certain brand of light bulbs in a photographic machine is normally distributed with a mean of 210 hours and a standard deviation on 50 hours.

    a) Determine the z-score of a light bulb that has a lifespan of exactly 124 hours?

    z= x - mean / standard deviation

    z= 124-210 / 50

    z= -86 / 50

    z= -1.72

    Z-Score is -1.72



    b) What is the probability that a randomly chosen light bulb would have a lifespan of less than 180 hours? (Not sure if correct)

    z= x- mean / Standard Deviation
    z= 180 - 210 / 50
    z= -0.60

    P(x<180) = P (z<-0.60) = 0.2258
    So there is a 0.2258 (22.58%) chance the lifespan is less than 180 hours.



    c) What is the probability that a randomly chosen light bulb would have a lifespan of between 200 and 250 hours? (Not sure if right, italic/bold part I'm a little iffy about)

    z= x - mean / standard deviation
    z= 200-210 / 50
    z= -0.2

    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

    There's a 0.3674 (36.74%) chance the lifespan is between 200 and 250.
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    Junior Member Bradyns's Avatar
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    Re: Questions Involving Z-Score, Can you please check my answer?

    A) Correct

    B) p = 0.27425

    C) Correct
    Last edited by Bradyns; April 21st 2013 at 01:47 PM.
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    Re: Questions Involving Z-Score, Can you please check my answer?

    Quote Originally Posted by Bradyns View Post
    A) Correct

    B) p = 0.27425

    C) Correct
    Can you tell me how you get 0.27425? On the Z-score table, the Z-score 0.6 has a probability of 0.2258? Or am I reading it wrong?
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  4. #4
    Junior Member Bradyns's Avatar
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    Re: Questions Involving Z-Score, Can you please check my answer?

    I used stattrek.com to get it that far, but my Standard normal distribution table gives me the same number to fewer decimal places.

    z = \frac{x - \mu}{\sigma}

    z = \frac{180 - 210}{50}

    z=-0.6

    Here's a pic of a standard normal distribution table.
    http://classes.engr.oregonstate.edu/...rmal_table.gif

    At '-0.6' you go to the '00' column as we are finding '-0.60'
    And it gives us a value for p [0.2743]
    Last edited by Bradyns; April 22nd 2013 at 12:39 PM.
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