Question

the brain volumes (cm³) of 20 brains have a mean of 1193.5 cm³ and a standard deviation of 126.4 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 1426.3 cm³ be significantly high? significantly low values are 940.7 cm³ or lower. (type an integer or a decimal. do not round.) significantly high values are □ cm³ or higher. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the range rule of thumb formula

The range rule of thumb states that values are significantly low if they are less than or equal to \(\bar{x}-2s\) and significantly high if they are greater than or equal to \(\bar{x} + 2s\), where \(\bar{x}\) is the mean and \(s\) is the standard deviation.
Given \(\bar{x}=1193.5\) and \(s = 126.4\)

Step2: Calculate the limit for significantly high values

We use the formula \(\bar{x}+2s\)
Substitute the values: \(1193.5+2\times126.4\)
First, calculate \(2\times126.4 = 252.8\)
Then, \(1193.5+252.8=1446.3\)

Answer:

Significantly high values are \(1446.3\mathrm{cm}^3\) or higher.
Since \(1426.3<1446.3\), a brain volume of \(1426.3\mathrm{cm}^3\) is not significantly high.