H2 maths qn

• quailmaster

  27 Mar 09, 12:37

  The mass of a sauce is normally distributed with mean 300g and standard deviation 10g and the mass of its bottle has an independent normal distribution with mean 80g and standard deviation 6g

  12 bottles of sauce are packed into a box. Assume empty box has negligible mass, find probability that a randomly chosen box weigh more than 4.5kg

   

  Correct ans is 0.931

  i tried but got 0.505

  Thanks in advance for your help

• wee_ws

  27 Mar 09, 13:05

  Hi,

    Answer is correct.

    Let M be mass of box. Then M ~ N( 12(300 + 80), 12(10^2 + 6^2) ).

    By GC, P(M > 4500) = 0.93126 = 0.931 (to 3 s. f.)

    Check your work again? Thanks!

  Cheers,
  Wen Shih

• quailmaster

  27 Mar 09, 13:10

  i got this guide book that says Var(aX + b) = a^2 Var(X)

  so for 12 bottles shouldnt it be (12^2)(10^2+6^2) ?

• quailmaster

  27 Mar 09, 13:43

  the same book says that Var(X +Y) = Var(X) + Var (Y)

  so can I just think of Var (12X) as Var ( X+ X + X +...12 times)

• wee_ws

  27 Mar 09, 15:39

  Hi,

    There are 12 bottles as stated in the problem statement, so there are 12 observations.

    We will then use Var(B_1 + ... + B_12) = 12 Var(B).

    If we use 12B, then it's not suitable as we are taking only one observation as our random variable.

    Hope that clarifies.

  Cheers,
  Wen Shih