We are given that the math scores of a standardized test follow a bell-shaped (normal) distribution with:

• Mean $\mu = 525$
• Standard deviation $\sigma = 110$

We need to find the percentage of test scores that are less than 415 or greater than 635.

Steps:

1. Convert raw scores to Z-scores: The Z-score formula is given by:

$Z = \frac{X - \mu}{\sigma}$

where:

• $X$ is the raw score,
• $\mu$ is the mean, and
• $\sigma$ is the standard deviation.

2. **Calculate the Z-s