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Math Help - Help with variance

  1. #1
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    Help with variance

    Hey guys, just asking two things here: a) can you please explain to me how to calculate the variance of certain things and b), can you put it into practice by answering the question below? Thanks!

    Baby Pty Ltd. is planning to launch a new brand of makeup product. Based on market research, if sales are high they can make a profit of $21.6 million per year. If sales are 'so so' they can make a profit of $5.4 million per year. Finally, if sales are low they can lose $2.9 million. The probabilities for the two profit scenarios are 0.55 and 0.22, respectively. Calculate the variance for the product.

    Thanks and regards,

    d
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Re: Help with variance

    I think this is related to the normal distribution? If so then I can proceed.

    The variance in a normal distribution is equal to: \text{Variance} = \sigma^2

    Otherwise, if you have a set of values, the formula for variance would be something completely different.
    For binomial distribution... \sigma^2 = npq

    For discrete data... \sigma^2 = \sqrt{\frac{\Sigma^2x}{n} - \frac{\Sigma x^2}{n^2}}

    And somehow, I always forget the one with grouped data ... but there are more.

    From the two values that you have, you will have to find the z score and from there, work out simultaneous equations:

    P(Z_1 < z) = 0.55

    Z_1 = 0.125

    0.125 is obtained from the normal table that is made available to you.

    P(Z_2 < z) = 0.22

    P(-Z_2 < z) = 0.78

    -Z_2 = 0.772

    Z_2 = -0.772

    And from that and the given equation: z = \frac{x-\mu}{\sigma}

    0.125 = \frac{21.6-\mu}{\sigma}

    0.772 = \frac{-2.9-\mu}{\sigma}

    You can find sigma and square it to get the variance.

    I will say it again, this is valid only if your problem deals with the normal distribution.
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  3. #3
    Grand Panjandrum
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    Re: Help with variance

    Quote Originally Posted by dylbagz View Post
    Hey guys, just asking two things here: a) can you please explain to me how to calculate the variance of certain things and b), can you put it into practice by answering the question below? Thanks!

    Baby Pty Ltd. is planning to launch a new brand of makeup product. Based on market research, if sales are high they can make a profit of $21.6 million per year. If sales are 'so so' they can make a profit of $5.4 million per year. Finally, if sales are low they can lose $2.9 million. The probabilities for the two profit scenarios are 0.55 and 0.22, respectively. Calculate the variance for the product.

    Thanks and regards,

    d
    First there are three profit scenarios high so-so and loss, and these have probabilities 0.55, 0.22 and 0.23.

    Let x denote the return which will be 21.6, 5.4 and -2.9 million dollars for each of the scenarios.

    The mean return:

    \mu=E(x)=0.55\times21.6+0.22\times5.4+0.23 \times (-2.9)

    and the variance is:

    \sigma^2=E((x-\mu)^2) =0.55\times(21.6-\mu)^2+0.22\times(5.4-\mu)^2+0.23 \times (-2.9-\mu)^2

    CB
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