Question

the brain volumes (cm³) of 20 brains have a mean of 1052.2 cm³ and a standard deviation of 124.9 cm³. 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 cm³ be significantly high? significantly low values are cm³ or lower (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall range - rule - of - thumb formula for significant limits

Significantly low values are $\mu - 2\sigma$ and significantly high values are $\mu+ 2\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Identify given values

We are given that $\mu = 1052.2$ $cm^{3}$ and $\sigma=124.9$ $cm^{3}$.

Step3: Calculate significantly low value

Use the formula $\mu - 2\sigma$. Substitute the values: $1052.2-2\times124.9=1052.2 - 249.8$.
$1052.2-249.8 = 802.4$ $cm^{3}$.

Answer:

$802.4$