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.

a. Assuming that years of education is normally distributed in the population, what proportion of working-class respondents have 12 to 16 years of education? What proportion of upper-class respondents have 12 to 16 years of education?
b. What is the probability that a working-class respondent, drawn at random from the population, will have more than 16 years of education? What is the equivalent probability for a middle-class respondent drawn at random?
c. What is the probability that a lower- or upper-class respondent will have less than 12 years of education?
d. Find the upper and lower limits, centered on the mean that will include 50% of all working-class respondents.
e. If years of education is actually positively skewed in the population, how would that change your other answers?

Lower class Working class Middle class Upper class Mean 1.61 12.80 14.45 15.45 Standard Deviation 2.67 2.85 3.08 2.98 123 697 626 38