For a very large sample of men, age 25-34, the average income was $29,800 and the SD was $14,400.

1) A typical starting salary for a lawyer graduating in the top of his or her class is about $80,000. What is this in standard units?

(80000 - 29800)/14400 = 3.48

2) In standard units, a particular person's income is -.54. What is her income?

-.54*14400 + 29800 = $22024

3) Approximately what percent of men in this age group have incomes in the range $15,400 to $45,200? (Assume that the distribution of income is apprxoimately symmetric.)

These incomes are both one SD away from the mean, and by the 68-95-99.7 rule, we know that roughly 68% of all observations will be within one SD of the mean.  So about 68% of men in this age group will have incomes in this range.

4) Again, assuming income distribution is approximately symmetric, about what percentage of men in this age group have incomes over $58600?
 

58600 is 2 SDs above average.  We know that about 95% of the observations are within two SDs of the mean, so 5% must be more than 2 SDs away from the mean.  Because we have assumed the distribution is symmetric, there should be the same percentage of people on each side of the mean, so we should have 2.5% above 58600.