Variance?

Problem: In a group of 160 women, their mean height was 63.6 inches with a variance of 6.25. Find the number of women with heights between 58.6 inches and 68.6 inches.

This is what I did: 6.25^2 = 12.5 63.6 + 2(12.5) = 88.6%

But after that I do not know what to do and I'm not sure if I'm doing it right.

Problem: In a group of 160 women, their mean height was 63.6 inches with a variance of 6.25. Find the number of women with heights between 58.6 inches and 68.6 inches.

This is what I did: 6.25^2 = 12.5 63.6 + 2(12.5) = 88.6%

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First, 6.25^2 does not equal 12.5.
Second, you cannot add a number to a “height” and get a “%” as a result.
This is irrelevant, however, because your approach is incorrect. It would be *very* advantageous for you to find a similar example problem in your text book and study it.

You need to first calculate the standard deviation. What is the relationship between standard deviation and variance? (Read your book.)

After finding the standard deviation, use it to calculate two “z-scores”, one for 58.6 inches and one for 68.6 inches. (Read your book.)

Use Table A (in your book) or your calculator to find the population percentages that the two z scores correspond to. Subtract the smaller one (for 58.6 inches) from the larger one (for 68.6 inches).