Question

The 2010 GSS provides the following statistics for the average years of education for lower-, working-, middle-, and upper-class respondents and their associated standard deviations. Assume that years of education are normally distributed in the population. Mean Standard Deviation N Lower-class 11.61 2.67 123 Working-class 12.80 2.85 697 Middle-class 14.45 3.08 626 Upper-class 15.45 2.98 38 How many years of education correspond to a Z score of +1.2 for upper-class respondents?

Answer 1

The answer is "18.087 years".

Explanation:

For upper class:

`\mu=15.45 \ years\\\\\alpha=2.98 \ years\\\\`

`P(Z \leq 1.2)` from the standard normal distribution on the table:

`P(Z \leq 1.2) =0.8849\\\\x=z_(\alpha)+\mu\\\\`

`=0.8849 * 2.98 +15.45\\\\ = 2.637002+15.45 \\\\=18.087 \ \ years\\`