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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This is what you need:|dw:1363253506385:dw|
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|
Not the answer you are looking for? Search for more explanations.
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:
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.
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...
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.
I had 32.238 < 32 < 32.838 as the 50% of egg lengths range. But, that is not the question.
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...
@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.
Oh, yes, I agree @ZeHanz. I had to go with the tools I had here.