Question

1. for a normally distributed dataset with a mean of 100 and a standard deviation of 10, what score corresponds to the 10th percentile?

a. 84.8
b. 90
c. 87.2
d. 92.5

Explanation:

Step1: Find the z - score for the 10th percentile

Looking up the 10th percentile (0.10) in the standard normal distribution table (z - table), the corresponding z - score is approximately $z=- 1.28$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the score we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 100$, $\sigma=10$, and $z=-1.28$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step3: Calculate the score $x$

Substitute the values into the formula: $x = 100+(-1.28)\times10=100 - 12.8 = 87.2$.

Answer:

C. 87.2