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Nurali

  • 3 years ago

The lengths of the eggs of a species of bird are roughly normally distributed, with a mean of 32 mm and an SD of 1.2 mm. Approximately 50% of the eggs have lengths in the range 32 mm plus or minus ____________ mm.

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  1. Nurali
    • 3 years ago
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    @Hero

  2. ZeHanz
    • 3 years ago
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    This is what you need:|dw:1363253506385:dw|

  3. ZeHanz
    • 3 years ago
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    To find out what the number on the dots is, you have to use a table or a graphical calculator like the TI-84. These have a built-in function that accepts a probability that is cumulative from the left:|dw:1363253885929:dw|

  4. ZeHanz
    • 3 years ago
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    In your case, because of the given middle 50%, the parts left and right of it, are 25%, so the cumulative probability (from the left) is 75%. Suppose L is the egg-length, then you would write it in mathematical notation as follows: \(P(L<0.75|~\mu =32,~\sigma=1.2)=x\). On the TI-84, you need the invNorm-function. Type in: \(invNorm(0.75, 32,1.2)\). Result: 32.81. Now, because of the symmetry of the normal distribution, you can answer the question.

  5. Nurali
    • 3 years ago
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    please answer.

  6. ZeHanz
    • 3 years ago
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    32 mm plus or minus ____________ mm. Because we've found the "plus" side of the 50% area to be 32.81 mm, 0.81mm has been added. Your answer will be 0.81. But: it is not quite clear what number of decimals are to be given, so it could also be 0.8 or 0.809. The calculator doesn't care: it gave me 32.8093877 as result from the invNorm function...

  7. Directrix
    • 3 years ago
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    I worked by hand using the tables and got 32 +/- .804. I did not interpolate. The standard deviation is tight about the mean. Somehow the answer did not feel right but I think it is okay.

  8. Nurali
    • 3 years ago
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    correct thanks

  9. Directrix
    • 3 years ago
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    I had 32.238 < 32 < 32.838 as the 50% of egg lengths range. But, that is not the question.

  10. ZeHanz
    • 3 years ago
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    I think in general the answer of the calculator is more accurate than that of a table, but there is no need to give many decimals if the standard deviation has only 1...

  11. Directrix
    • 3 years ago
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    @Nurali --> My @signal does not work. Send a web mail or note message if you need my help. Unless I happen to see that you called me, I don't know.

  12. Directrix
    • 3 years ago
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    Oh, yes, I agree @ZeHanz. I had to go with the tools I had here.

  13. jishan
    • 3 years ago
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    not clear

  14. ZeHanz
    • 3 years ago
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    @jishan: what do you mean?

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