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.\nwhat is the height of a child with a z-score of 1.5?\nenter your answer, rounded to the nearest tenth, in the box.\n 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 we want to find, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.
Step2: Rearrange to solve for $x$
Rearrange the formula to isolate $x$: $x = z\sigma + \mu$
Step3: Substitute given values
Substitute $z=1.5$, $\sigma=2.4$, and $\mu=54$: $x = (1.5 \times 2.4) + 54$ $x = 3.6 + 54$ $x = 57.6$
Answer:
57.6 in.