So I am working on this question but I don't know how to apply the Empirical Rule.
Question: A Cornell University researcher measured the mouth volumes of a large number of men and women and reported that the distribution of the mouth volumes for men is approximately bell-shaped with a mean of 66 cc and a standard deviation of 17 cc. Moreover, the distribution of the mouth volumes for women is also approximately bell-shaped with a mean of 54 cc and a standard deviation of 14.5 cc.
a) Applying the Empirical Rule, what percentage of man has mouth volume over 100 cc or less than 49 cc?
Now this is what I did.
100-66=34 which is 2(17). Thus, 100 is 2 standard deviation to the right of the mean.
66-49=17 which is 1(17). Thus, 17 is 1 standard deviation below the mean
From here, I don't know which formula to apply to get the percentage that I did for this question. So can someone help me solve this.
Thank you.
The empirical rule can be broken down into three parts: $(1):$ $68\%$ of data falls within the first standard deviation from the mean; $(2):$ $95\%$ fall within two standard deviations; $(3):$ $99.7\%$ fall within three standard deviations.
From $(1)$ and the fact that the Normal distribution is symmetric, it follows that $16\%$ will be above one standard deviation and $16\%$ bellow. From $(2)$ it follows that $2.5\%$ will be above two standard deviations and $2.5\%$ bellow.