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anonymous

  • one year ago

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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  1. phi
    • one year ago
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    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?

  2. anonymous
    • one year ago
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    i was able to find the mean.. but the variance was not correct

  3. phi
    • one year ago
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    to find the variance, for find the variance of the wine and of the rack what do you get for them ?

  4. anonymous
    • one year ago
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    is that 1.02 ?? help me in calculating the variance... the rest i can do..

  5. anonymous
    • one year ago
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    in the answer the variance is 0.1332

  6. phi
    • one year ago
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    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?

  7. anonymous
    • one year ago
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    wait

  8. anonymous
    • one year ago
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    0.00036

  9. phi
    • one year ago
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    too many zeros. 0.06*0.06= 0.0036

  10. anonymous
    • one year ago
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    yes sorry 1 zero in excess

  11. phi
    • one year ago
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    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 ?

  12. anonymous
    • one year ago
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    thank you very much.. it was my homework..

  13. phi
    • one year ago
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    we are not done. Can you finish this?

  14. anonymous
    • one year ago
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    yes of course.. i know the rest.. i was having problem with the variance.. i forgot to square them..

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