H2 maths qn

quailmaster SG

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 SG

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 SG

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 SG

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 SG

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