Question

adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. find the height of a man with a z - score of - 1.8929 (to 4 decimal places)

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 value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to solve for $x$. Rearranging the formula gives $x = z\sigma+\mu$.

Step2: Substitute given values

We are given that $\mu = 69.0$, $\sigma=2.8$, and $z=-1.8929$. Substitute these values into the formula: $x=-1.8929\times2.8 + 69.0$.

Step3: Perform the calculation

First, calculate $-1.8929\times2.8=-5.30012$. Then, $x=-5.30012 + 69.0=63.6999$.

Answer:

$63.7000$