Question

find the number of standard deviations from the mean. round your answer to two decimal places.

1. the test scores on the chapter 10 mathematics test have a mean of 52 and a standard deviation of 10. andrea scored 86 on the test. how many standard deviations from the mean is that?

a) 0.49 standard deviations below the mean
b) 3.40 standard deviations above the mean
c) 3.40 standard deviations below the mean
d) 0.49 standard deviations above the mean

Explanation:

Step1: Recall z - score formula

The formula to find the number of standard deviations a value $x$ is from the mean $\mu$ is $z=\frac{x - \mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard - deviation, and $z$ is the number of standard deviations from the mean.

Step2: Identify given values

We are given that $\mu = 52$, $\sigma=10$, and $x = 86$.

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{86 - 52}{10}=\frac{34}{10}=3.40$. Since $z>0$, the score is above the mean.

Answer:

B. 3.40 standard deviations above the mean