https://file.aiquickdraw.com/mathbot/file/1729296117912tki1xw3t.jpg

We are asked to find the proportion of students who scored less than 350 on the math section of the SAT. Given the information:

- Mean \(\mu = 528\)
- Standard deviation \(\sigma = 117\)
- We need to find the proportion of scores less than 350.

This involves calculating the **Z-score** for 350 and then using the standard normal distribution table to find the corresponding proportion.

The formula for the Z-score is:

\[
Z = \frac{X - \mu}{\sigma}
\]

Where:
- \( X = 350 \) (the score we are interested in),
- \( \mu = 528 \) (the mean),
- \( \sigma = 117 \) (the standard deviation).

Substituting the values:

\[
Z = \frac{350 - 528}{117} = \frac{-178}{117} \approx -1.521
\]

Now, we look up the Z-score of -1.521 in the standard normal distribution table (or use a calculator). The proportion corresponding to \( Z = -1.521 \) is approximately **0.064**.

So, about **6.4%** of students scored less than 350 on the math section of the SAT.

Rounded to four decimal places, the answer is:

\[
\boxed{0.0640}
\]

Would you like further details or clarifications?

### Related Questions:
1. How do you interpret a Z-score in the context of a normal distribution?
2. What proportion of students scored between 350 and 528 on the math section?
3. What is the probability that a student scores above 600?
4. How would the proportion change if the standard deviation were larger?
5. What is the significance of a normal distribution in analyzing standardized test scores?

**Tip:** Understanding how Z-scores map to probabilities helps in making sense of how rare or common certain scores are in a normal distribution.

About what proportion of students who took the SAT scored less than 350 on the math section?

This problem asks for the proportion of students who scored below 350 on the math section of the SAT, given a mean of 528 and a standard deviation of 117. Learn how to calculate Z-scores and find probabilities in a normal distribution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation