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?

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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