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The Normal distribution – Management Accounting (MA)

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  1. Excuse me, sir.
    I think we have a small matter in Example 3:
    50% of 95% must be equal to 47.5% (0.475 => z= 1.96).
    Length = 1.96 x 0.2 = 0.392
    X = 10 – 0.392 = 9.608
    So, there is a 95% probability that the length will be more than 9.608 cms.

    Please help us re-check, sir.
    Thank you so much.

    • 50% of 10cm is indeed 5cm, but that is not what the question is asking for.

      It is asking what proportion of all the units will have a length of 10cm, and because 10cm is the average it means that half (50%) of the units are longer than 10cm, and half of them are less than 10cm.

  10. Greetings sir,

    I feel the answer should have been calculated by adding the z to the mean, and not subtracting it.

    z = (x – xbar)/sd
    1.645 = (x – 10) / 0.2
    1.645×0.2 = x – 10
    0.329 = x – 10
    0.329 + 10 = x
    10.329 = x

    • If you are referring to example 3, then that cannot possibly be the answer.

      There is a 50% chance of being more than 10, so how can there possibly be a bigger chance of it being more than 10.329? It would make no sense at all.

      • The algebra of the formula shows another answer as demonstrated. If you don鈥檛 agree, how do you reply to the working I showed you ?

        Perhaps we could say, that 50% chance there is of it being below 10 – as it is above as the distribution is symmetrical, and then we apply the first 50% to below 10, and the balance of the probability of the 95%, ie 45% to above the 10.

        In the end, shouldn鈥檛 the interpretation of the probability distribution be subject to the formula calculation ?

        Awaiting your reflection and suggestion.
        Thankyou.

      • You cannot learn this just as playing with algebra.
        Draw the curve in the way that I do in my lecture – the answer could not possibly by 10.329 as I wrote before.

      • So that means if theres 50% more chances that its more than 10cm then in that case the formula would be
        Z=10-x divide by 0.2
        ?

      • As I wrote before, there is no point whatsoever in simply learning formula without understanding.

        The z value is the different between the mean and the point being considered, divided by the standard deviation.
        Because the curve is symmetrical it is irrelevant when calculating the z value whether the point being considered is more or less than the mean.

    • the application used to derive the algebraic expression is wrong. we know that 50% is above the mean. and the probability than the length will be more than X is 95%, meaning that the point x is bellow 10cm and in the expression for the Z score you need to subtract the X from the average (10cm)

      Z =(10-x)/0.20
      where z=1.645
      1.645=(10-X)/0.20
      1.645*0.20=10-X
      0.329 = 10-X
      X=10-0.329
      X=9.671

      which is same as the lecturer

  11. A new topic for me, but you explained it so well as always. I was so confused initially reading the example questions but had a few “aha moments” during the lecture. So thank you for helping me to get my head around it. 馃檪

  12. sir,in determining the proportions of what is less than a mean(say 9.8 as in example2) can you work with the value directly by dividing with SD as done for those above and then change to standard form. like 9.8/0.2=49(4.9*10^1 then look up in the table just like in logarithms and indices).

  13. Hi sir,
    Please explain this questions.
    Q1)A normal distribution has a mean of 75and a variance of 25.
    what is the upper quartile of this distribution?
    Q2)A normal distribution has mean of 150,and a standard deviation of 20.
    80% of the distribution is below which of the following (approximately)?

    • In future please ask this kind of question in the Ask the Tutor forum, and not as a comment on a lecture.

      For the first question you need to find the value that has a probability of 25% (0.25) of being above the mean.
      For the second question you need to find the value that has a probability of 80 – 50 = 30% (0.30) below the mean.

      In both cases you need to work backwards in the tables to find the number of standard deviations (the z score) in the way I explain in the lectures.

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