Question

The brain volumes (cm³) of 20 brains have a mean of 1118.8 cm³ and a standard deviation of 129.9 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 1358.6 cm³ be significantly high?

Significantly low values are ____ cm³ or lower. (Type an integer or a decimal. Do not round.)

Answer 1

Significantly low values for brain volumes are 859.0 cm³ or lower, calculated using the range rule of thumb with a mean of 1118.8 cm³ and a standard deviation of 129.9 cm³. A volume of 1358.6 cm³ is not significantly high.

Step-by-step explanation:

The question involves using the range rule of thumb to determine the limits for significantly low or high brain volumes. Given the mean brain volume is 1118.8 cm³ and the standard deviation is 129.9 cm³, the range rule of thumb states that most values lie within two standard deviations of the mean. To find the limits for significantly low or high values, we calculate:

• Significantly low values: Mean - 2(Standard Deviation) = 1118.8 cm³ - 2(129.9 cm³) = 1118.8 cm³ - 259.8 cm³ = 859.0 cm³
• Significantly high values: Mean + 2(Standard Deviation) = 1118.8 cm³ + 2(129.9 cm³) = 1118.8 cm³ + 259.8 cm³ = 1378.6 cm³

Therefore, significantly low values are 859.0 cm³ or lower. A brain volume of 1358.6 cm³ would not be considered significantly high since it is below the high limit of 1378.6 cm³.