The incomes of trainees at a local mill are normally distributed with a mean of \( \$ 1,100 \) and a standard deviation \( \$ 150 \). What percentage of trainees earn more than \( \$ 900 \) a month? \( 90.82 \% \) \( 35.31 \% \) \( 9.18 \% \) \( 42.57 \% \) \( 64.69 \% \)

To find the percentage of trainees earning more than $900, we first calculate the z-score using the formula: \[ z = \frac{(X - \mu)}{\sigma} = \frac{(900 - 1100)}{150} = \frac{-200}{150} = -1.33 \] Using standard normal distribution tables or software, we find that the area to the left of \( z = -1.33 \) is approximately \( 0.0918 \) or \( 9.18\% \). Thus, the percentage of trainees earning more than $900 is: \[ 100\% - 9.18\% = 90.82\% \] So, the answer is \( 90.82\% \). If you're ever faced with finding z-scores, remember it’s just a simple transformation of the raw score into a standardized score. Always make sure to double-check whether you need to find the area to the left or right of your z-score, as that can shift your final percentage significantly! Calculating percentages based on the normal distribution involves knowing your mean and standard deviation, but it’s also helpful to plot your values on a bell curve. Visualizing it not only solidifies your understanding but can make the question feel more tangible. Plus, using a graph can help reveal other insights about the distribution you might want to explore!