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Help with a probability question. (CIE S2)

Discussion in 'Mathematics' started by andymiller82, Mar 15, 2020.

  1. andymiller82

    andymiller82 New commenter

    I'm teaching the Cambridge specification of S2 for the first time after teaching Edexcel previously. If anyone is able to clarify this for me I'd be very grateful. It is no doubt something simple that I am missing.

    Worked Example 3.9 on page 63 of the Cambridge Probability and Statistics 2 book:

    “A gift package contains a set of three bars of soap. The mass, in grams, of each bar of soap is given by S~N(50,4^2) and the packaging by T~N(90,5^2). The gift package can be posted at a cheap rate if the mass is under 250g. Assuming that S and T are independent, find the probability that a randomly chosen gift package can be posted at the cheap rate.”

    Ok so the worked examples gives Var(3S+T) as 3^2*4^2 + 5^2. Fine.

    From the June 2016 CIE S2 Exam paper Q7 (i):

    “Bags of sugar are packed in boxes, each box containing 20 bags. The masses of the boxes, when empty, are normally distributed with mean 0.4kg and standard deviation 0.01kg The masses of the bags are normally distributed with mean 1.02kg and standard deviation 0.03kg.

    (i) Find the probability that the total mass of a full box of 20 bags is less than 20.6kg."

    To me this looks like the same type of question as the worked example from the book and I thought it would be

    Var(20 Bags + 1 box) = 20^2*0.03^2+0.01^2

    But the marking scheme gives the variance as 20*0.03^2+0.01^2.

    My question is, how are these two questions different and how do I know if I should be squaring the coefficient or not?

    Thanks so much to anyone who takes the time to read this and help me out.
  2. andymiller82

    andymiller82 New commenter

    I'm starting to think that the example in the book is wrong and because the observations of the variable are independent then it should just be 3 * Var(S). If anyone can confirm then do let me know.
    bombaysapphire likes this.
  3. gainly

    gainly Star commenter

    For the sum or difference of independent variables:


    So the example in the book is wrong as you thought,
  4. andymiller82

    andymiller82 New commenter

    Thanks for taking the time to reply to me! Good to get a second opinion. I've got it now, and more importantly, my student now understands it as well.

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