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 □ cm³ or lower. (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 \( \mu - 2\sigma\) or lower, and significantly high if they are \( \mu+ 2\sigma\) or higher, where \( \mu\) is the mean and \( \sigma\) is the standard deviation.
Given \( \mu = 1193.5\) and \( \sigma=126.4\)

Step2: Calculate the lower limit

For significantly low values: \( \mu - 2\sigma=1193.5-2\times126.4\)

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Answer:

Significantly low values are \(940.7\) \(cm^{3}\) or lower.