1. The problem involves understanding the sign of $z$-scores in relation to percentages in a normal distribution. 2. When $z$ is negative, it corresponds to values below the mean, so the percentage represents the bottom portion of the distribution. 3. When $z$ is positive, it corresponds to values above the mean, so the percentage represents the top portion of the distribution. 4. Therefore, if you are looking for the top percentage, the $z$-score will be positive. 5. Conversely, if you are looking for the bottom percentage, the $z$-score will be negative. This is because the $z$-score measures how many standard deviations a value is from the mean, with negative values below and positive values above the mean.