Question

The brain volumes ​(cm cubed​) of 20 brains have a mean of 1067.9 cm cubed and a standard deviation of 121.9 cm cubed. 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 1341.7 cm cubed be significantly​ high?

Answer 1

The limit for a significantly low volume is 824.1 cm^3 and the limit for a significantly high volume is 1311.7 cm^3.

A value of 1341.7 cm^3 is above the upper bound, so it will be considered significantly high.

Explanation:

The range rule of thumb considers that the range (the difference between the maximum value and the minimum value) has a value of aproximately 4 times the standard deviation. That is that the limits of the expected values will be in the interval within 2 standards deviation above and below the mean.

Then, using this rule, we will consider that the brain volumes are significantly low if they are 2 standard deviations below the mean, and significantly high if they are 2 standard devitions above the mean.

Then, we can define the lower bound as:

`LB=\mu-2\sigma=1067.9-2\cdot121.9=1067.9-243.8=824.1`

And the upper bound as:

`UB=\mu+2\sigma=1067.9+2\cdot121.9=1067.9+243.8=1311.7`

A value of 1341.7 cm^3 is above the upper bound, so it will be considered significantly high.