Nurali
  • Nurali
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.
Mathematics
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SOLVED
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chestercat
  • chestercat
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Nurali
  • Nurali
@Hero
ZeHanz
  • ZeHanz
This is what you need:|dw:1363253506385:dw|
ZeHanz
  • ZeHanz
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|

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ZeHanz
  • ZeHanz
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.
Nurali
  • Nurali
please answer.
ZeHanz
  • ZeHanz
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...
Directrix
  • Directrix
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.
Nurali
  • Nurali
correct thanks
Directrix
  • Directrix
I had 32.238 < 32 < 32.838 as the 50% of egg lengths range. But, that is not the question.
ZeHanz
  • ZeHanz
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...
Directrix
  • Directrix
@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.
Directrix
  • Directrix
Oh, yes, I agree @ZeHanz. I had to go with the tools I had here.
anonymous
  • anonymous
not clear
ZeHanz
  • ZeHanz
@jishan: what do you mean?

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