Question

the brain volumes ($cm^{3}$) of 20 brains have a mean of 1052.2 $cm^{3}$ and a standard deviation of 124.9 $cm^{3}$. use the given standard deviation and the range - rule of thumb to identify the limits separating values that are significantly low or significantly high. for such data, would a brain volume of 1272.0 $cm^{3}$ be significantly high? significantly low values are 802.4 $cm^{3}$ or lower. (type an integer or a decimal. do not round.) significantly high values are $\square cm^{3}$ or higher. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the range - rule - of - thumb for significant values

According to the range - rule - of - thumb, significant low values are $\mu - 2\sigma$ or lower and significant high values are $\mu+ 2\sigma$ or higher, where $\mu$ is the mean and $\sigma$ is the standard deviation.
We are given that $\mu = 1052.2$ and $\sigma=124.9$.

Step2: Calculate the significant high value

Use the formula $\mu + 2\sigma$.
Substitute the given values: $1052.2+2\times124.9$.
First, calculate $2\times124.9 = 249.8$.
Then, $1052.2+249.8=1302$.

Answer:

$1302$