Question

section 3.4 homework score: 4/14 answered: 4/14 question 5 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 - 1.25 (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 $x$.

Step2: Rearrange the formula for $x$

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$ to get $z\sigma=x-\mu$. Then, adding $\mu$ to both sides gives $x=\mu + z\sigma$.

Step3: Substitute the given values

We are given that $\mu = 69.0$, $z=-1.25$, and $\sigma = 2.8$. Substituting these values into the formula $x=\mu+z\sigma$, we have $x = 69.0+(-1.25)\times2.8$.

Step4: Calculate the value of $x$

First, calculate $(-1.25)\times2.8=-3.5$. Then, $x = 69.0-3.5=65.5000$.

Answer:

$65.5000$