Question

examples: percentages to raw data

1. on the most recent test, a student scored in the 40th percentile. the mean of the test scores was an 85 and the standard deviation was 1.5. what was the student’s score?

Explanation:

Step1: Find the z - score

We use a standard normal distribution table (z - table). The 40th percentile corresponds to a z - score. Looking up the value in the z - table, the z - score $z$ for the 40th percentile is approximately $z=-0.25$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 85$, $\sigma=1.5$, and $z=-0.25$. Rearranging the formula for $x$ gives $x=\mu+z\sigma$.

Step3: Calculate the raw score

Substitute the values into the formula: $x = 85+(- 0.25)\times1.5=85 - 0.375 = 84.625$.

Answer:

$84.625$