3.a) Duane's score is transformed to
z = (84 - 80)/4 = 4/4 = 1.00
3.b) Debbie's score transforms to
z = (90 - 85)/8 = 5/8 ≈ 0.63
3.c) Duane's score is relatively higher than Debbie's, since his standardized (z) score is higher. (Recall that z-scores corresponds to a normally distributed random variable with mean 0 and s.d. 1.)
4. The p-th percentile of any given distribution refers to the top (100 - p)% of the distribution. So if the 75th percentile of SAT scores is 1400, this means that the top 25% of scores are above 1400.
