A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 316 and a standard deviation of 44. 

What proportion of students taking the exam receive a score that is within 72 points of the mean?

 

Round your answer to four (4) decimal places. (e.g.  0.1234)

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

A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 316 and a standard deviation of 44. What proportion of students taking the exam receive a score that is within 72 points of the mean? Round your answer to four (4) decimal places. (e.g. 0.1234)

Calculate the proportion of students scoring within 72 points of the mean on a standardized test with scores normally distributed. The problem involves understanding normal distribution, using Z-scores, and applying the Empirical Rule. Suitable for students in Grades 10-12.

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