Question

Solve using a TI-83 or 84 calculator. One area of inquiry in the field of evolutionary biology deals with human mating habits, and the preferences we use in selecting a romantic partner. Both genders place a high value on looks in their mate selection process, and a scale has been developed to quantify the looks rating. The possible scores range from 0 to 25, where the population mean is 12.5 and the population standard deviation is 4.5. The distribution of scores is Normal. Use the Empirical rule to find the following (it might be helpful to make a sketch):
a. Approximately what percent of the population has a looks rating between 8 and 17?
b. Approximately what percent of the population has a looks rating of 17 or higher?

Answer 1

Using the empirical rule, we know that approximately 68%, 95% and 99.73% of observations lie within one, two and three standard standard deviations from the mean respectively.

a)

Now,

This means approximately 68% observations lie between 8 and 17.

b)

Also,

So, proportion of observation below 17 = i.e. 84%

{Proportion of observations lying on the left side of the mean + Proportion of observations lying between 0 and 17}

So, Percentage of population having a rating 17 or higher = 100-84 = 16%