a study of adult males found their head circumferences to be normally distributed, with a mean of 57.5…
a study of adult males found their head circumferences to be normally distributed, with a mean of 57.5 centimeters and a standard deviation of 1.5 centimeters. jacks head has a circumference in the 16th percentile. how many centimeters is his head circumference? give your answer to the nearest tenth.
Answer
Answer:
56.0
Explanation:
Step1: Use z - score table
The 16th percentile corresponds to a z - score of approximately $z=- 1$.
Step2: Apply z - score formula
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 57.5$, $\sigma=1.5$, and $z = - 1$. We can rewrite the formula for $x$: $x=\mu+z\sigma$.
Step3: Calculate $x$
Substitute the values into the formula: $x = 57.5+( - 1)\times1.5=57.5 - 1.5=56.0$.