Question

The brain volumes (cm3) of 20 brains have a mean of 1189.3cm3 and a standard deviation of 125.5cm3. Use the range rule of thumb to identify the limits seperating values that are significantly high or significantly low. For such data, would a brain volume of 1409.7cm3 be significantly high?

Answer 1

The range rule of thumb estimates the range of significantly high or low values in a data set based on the standard deviation. A brain volume of 1409.7cm3 is not significantly high based on the given data.

Step-by-step explanation:

The range rule of thumb is a rough estimate of the range of values that can be considered significantly high or low in a data set based on the standard deviation. It states that about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations.

In this case, the mean brain volume is 1189.3cm3 and the standard deviation is 125.5cm3. To find the range of values that are significantly high, we can add and subtract three times the standard deviation from the mean: 1189.3 + (3 * 125.5) = 1565.8cm3. Therefore, any brain volume greater than 1565.8cm3 would be considered significantly high.

Since 1409.7cm3 is less than 1565.8cm3, it would not be considered significantly high.