Question

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 1

Z= (X-mean)/s.d.

X (height in inches) = (Z*sd)+mean = (1.5*2.4)+54 = 57.6 in

Answer 2

We have been given that 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.

We are asked to find out height of a child with a z-score of 1.5.

Since we know we can find out height a child using z score formula.

$z=\frac{x- \mu }{\sigma}$, where z represents z score, x represents the value we want to find out z score of, $\mu$ represents mean of the data and $\sigma$ represents standard deviation of data.

Upon substituting our given values in this formula we will get,

$1.5=\frac{x-54}{2.4}\\ \\ 1.5\cdot 2.4= x- 54\\ \\ 3.6=x-54\\ \\ x=3.6+54=57.6$

Therefore, height of the child with a z score of 1.5 will be 57.6 inches.