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.

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- anonymous

- schrodinger

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- phi

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?

- anonymous

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

- phi

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

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- anonymous

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

- anonymous

in the answer the variance is 0.1332

- phi

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?

- anonymous

wait

- anonymous

0.00036

- phi

too many zeros. 0.06*0.06= 0.0036

- anonymous

yes sorry 1 zero in excess

- phi

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 ?

- anonymous

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

- phi

we are not done. Can you finish this?

- anonymous

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

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