Answer:
1.
a) A score that is 6 points above the mean corresponds to a z-score of (6 / 12) = 0.5.
b) A score that is 18 points below the mean corresponds to a z-score of (-18 / 12) = -1.5.
2.
a) To find the score that represents the 75th percentile for the raw scores, we can use the standard normal table or the Z-table. Since the raw scores form a normal distribution with a mean of 50 and a standard deviation of 4, we can standardize the scores to find the corresponding z-score.
The 75th percentile corresponds to a z-score of 0.67 (by using the standard normal table or the Z-table).
So the raw score that represents the 75th percentile is (0.67 * 4) + 50 = 52.68
Note: Percentile rank is a way to describe the relative standing of a value within a distribution, it's the percentage of values that are equal to or below the value in question.