anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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phi
  • 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
  • anonymous
i was able to find the mean.. but the variance was not correct
phi
  • 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
  • anonymous
is that 1.02 ?? help me in calculating the variance... the rest i can do..
anonymous
  • anonymous
in the answer the variance is 0.1332
phi
  • 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
  • anonymous
wait
anonymous
  • anonymous
0.00036
phi
  • phi
too many zeros. 0.06*0.06= 0.0036
anonymous
  • anonymous
yes sorry 1 zero in excess
phi
  • 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
  • anonymous
thank you very much.. it was my homework..
phi
  • phi
we are not done. Can you finish this?
anonymous
  • anonymous
yes of course.. i know the rest.. i was having problem with the variance.. i forgot to square them..

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