the heights of the children at a summer camp are normally distributed with a mean of 54 inches and a…
the heights of the children at a summer camp are normally distributed with a mean of 54 inches and a standard deviation of 2.4 inches. what is the height of a child with a z - score of 1.5? enter your answer, rounded to the nearest tenth, in the box. in.
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 value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to find $x$, so we can re - arrange the formula to $x = z\sigma+\mu$.
Step2: Substitute given values
We are given that $\mu = 54$, $\sigma=2.4$, and $z = 1.5$. Substitute these values into the formula $x=z\sigma+\mu$. $x=1.5\times2.4 + 54$
Step3: Calculate the value of x
First, calculate $1.5\times2.4=3.6$. Then, $x=3.6 + 54=57.6$.
Answer:
$57.6$