use the information given in the table on the right to complete each of the following statements. brenda is…
use the information given in the table on the right to complete each of the following statements. brenda is 50 inches tall. her z - score is 0.5. zach has a z - score of - 1.5. his height is inches.
Answer
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 want to find $x$, so we can re - arrange the formula to $x=\mu+z\sigma$.
Step2: Identify values from the table
We are given that $\mu = 49$ inches (mean height), $\sigma = 2$ inches (standard deviation), and $z=-1.5$ (Zach's z - score).
Step3: Calculate Zach's height
Substitute the values into the formula $x=\mu + z\sigma$. So $x = 49+( - 1.5)\times2$. First, calculate $( - 1.5)\times2=-3$. Then $x = 49-3=46$ inches.
Answer:
46