Question

analyzing test scores using a normal distribution curve
a normal distribution curve, where $\overline{x}=70$ and $\sigma = 15$, was created by a teacher using her students grades. what information about their performances can be obtained by analyzing the curve?

Explanation:

A normal distribution curve shows the spread of data. The mean ($\bar{x} = 70$) is the central value. The standard deviation ($\sigma=15$) measures the variability. Using the empirical rule:

• About 68% of scores lie within $\bar{x}\pm\sigma$ (55 - 85).
• About 95% within $\bar{x}\pm2\sigma$ (40 - 95).
• About 99.7% within $\bar{x}\pm3\sigma$ (25 - 105).

This helps understand typical scores (around 70), common score range (e.g., 55 - 85 for 68% of students), and rare scores (outside 25 - 105).

Answer:

By analyzing the curve, we can know that about 68% of students' scores are between 55 and 85, about 95% between 40 and 95, and about 99.7% between 25 and 105. The mean score is 70, which is the central tendency of the data.