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Math Help - How to find Standard Deviation?

  1. #1
    wby
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    How to find Standard Deviation?

    In a population of men, their heights are normally distributed with a mean of 178 cm. If a man with a height of 184 cm is shorter than 20% of the population, determine the standard deviation of the population.
    the answer is 8.3cm, but how do u do it with a graphic-calculator (TI series)?
    if I use this formula, z=(x-mean)/standard deviation, the answer is 30, which is not the right answer, can anyone tell me why?
    Thank you!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wby View Post
    In a population of men, their heights are normally distributed with a mean of 178 cm. If a man with a height of 184 cm is shorter than 20% of the population, determine the standard deviation of the population.
    the answer is 8.3cm, but how do u do it with a graphic-calculator (TI series)?
    if I use this formula, z=(x-mean)/standard deviation, the answer is 30, which is not the right answer, can anyone tell me why?
    Thank you!
    Look up the z-score z_{80} such that p(z<z_{80})=0.8 (he is taller than 80% of the population). My tables tell me that this is 0.851.

    Now the z-score corresponding to 184 \mbox{ cm} is:

    <br />
z=\frac{184-178}{\sigma}=0.841<br />

    so \sigma = 6/0.841 = 7.13 \mbox{ cm}

    RonL
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  3. #3
    wby
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    Thank you, but do you know how to get the 0.841 on a graphic calculator?
    (binomial pdf, normal pdf, normal inverse perhaps?)
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by wby View Post
    Thank you, but do you know how to get the 0.841 on a graphic calculator?
    (binomial pdf, normal pdf, normal inverse perhaps?)
    No, but it is something like invnormaldis(0.8) that is inverse cumulative normal
    of 0.8.

    RonL
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  5. #5
    wby
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    thank you!
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