## Nurali 2 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.

1. Nurali

@Hero

2. ZeHanz

This is what you need:|dw:1363253506385:dw|

3. 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|

4. 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.

5. Nurali

6. 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...

7. 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.

8. Nurali

correct thanks

9. Directrix

I had 32.238 < 32 < 32.838 as the 50% of egg lengths range. But, that is not the question.

10. 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...

11. 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.

12. Directrix

Oh, yes, I agree @ZeHanz. I had to go with the tools I had here.

13. jishan

not clear

14. ZeHanz

@jishan: what do you mean?