Question

Bottles of wine are stacked in racks of 12. The weights of these bottles are normally distributed with
mean 1.3 kg and standard deviation 0.06 kg. The weights of the empty racks are normally distributed
with mean 2 kg and standard deviation 0.3 kg.
(i) Find the probability that the total weight of a full rack of 12 bottles of wine is between 17 kg and
18 kg.

Answer 1

The total weight is the sum of two normally distributed values

The first step is to find the mean and std dev of total weight.

The mean will be the mean of the two distributions that you are adding
the variance (square of std) will be the sum of the two variances

Can you find the mean and variance of the total weight?

Answer 2

i was able to find the mean.. but the variance was not correct

Answer 3

to find the variance, for find the variance of the wine and of the rack
what do you get for them ?

Answer 4

is that 1.02 ?? help me in calculating the variance... the rest i can do..

Answer 5

in the answer the variance is 0.1332

Answer 6

wine: mean 1.3 kg and standard deviation 0.06 kg.
the variance of the wine is the standard deviation squared (multiplied by itself)
what do you get for the variance of the wine?

Answer 7

wait

Answer 8

0.00036

Answer 9

too many zeros. 0.06*0.06= 0.0036

Answer 10

yes sorry 1 zero in excess

Answer 11

so the statistics for a *bottle* is mean 1.3 kg, var 0.0036
we need the statistics for 12 bottles. Add up those numbers 12 times (or simply multiply each by 12). what do you get ?

Answer 12

thank you very much.. it was my homework..

Answer 13

we are not done. Can you finish this?

Answer 14

yes of course.. i know the rest.. i was having problem with the variance.. i forgot to square them..