Question

the brain volumes (cm³) of 20 brains have a mean of 1186.6 cm³ and a standard deviation of 120.7 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 1478.0 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 for significant values

The range rule of thumb states that significantly low values are \( \text{mean} - 2\times\text{standard deviation} \) and significantly high values are \( \text{mean} + 2\times\text{standard deviation} \). We first calculate the limit for significantly low values.

Given: mean (\( \mu \)) = 1186.6 \( \text{cm}^3 \), standard deviation (\( \sigma \)) = 120.7 \( \text{cm}^3 \)

Step2: Calculate the lower limit

Using the formula for significantly low values: \( \mu - 2\sigma \)

Substitute the values: \( 1186.6 - 2\times120.7 \)

First, calculate \( 2\times120.7 = 241.4 \)

Then, \( 1186.6 - 241.4 = 945.2 \)

Answer:

945.2