Question

the scores on a mathematics exam have a mean of 69 and a standard deviation of 7. find the x - value that corresponds to the z - score - 2.33. round the answer to the nearest tenth.

a. 66.7
b. 85.3
c. 52.7
d. 62.0

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the data - value, $\mu$ is the mean, and $\sigma$ is the standard deviation. We need to solve for $x$. Rearranging the formula gives $x = z\sigma+\mu$.

Step2: Substitute given values

We are given that $\mu = 69$, $\sigma = 7$, and $z=-2.33$. Substitute these values into the formula: $x=-2.33\times7 + 69$.

Step3: Perform the calculation

First, calculate $-2.33\times7=-16.31$. Then, $x=-16.31 + 69=52.69$.

Step4: Round the result

Rounding $52.69$ to the nearest tenth gives $52.7$.

Answer:

C. 52.7