We are asked to find the proportion of students who receive a score within 72 points of the mean on a standardized test where the scores are normally distributed.

Given information:

• Mean ($\mu$) = 316
• Standard deviation ($\sigma$) = 44
• We need the proportion of students with scores within 72 points of the mean, i.e., between $316 - 72$ and $316 + 72$.

Step 1: Define the bounds

The lower bound is: $316 - 72 = 244$ The upper bound is: $316 + 72 = 388$ Thus, we are looking for the probability that a score is between 244 and