Question

Suppose that the mean cranial capacity for men is 1070cc ( cubic centimeters) and that the standard deviation is 200cc. Assuming that men's cranial capacities are normally distributed complete the following statements in (A) choose one ( ?, 68%, 75%, 95%, 99.7%)Answer (B) also

Answer 1

Mean (μ): 1070 cc

Standard deviation (σ): 200 cc

(a)

We need to calculate the percentage of men that have a cranial capacity between 870 cc and 1270 cc.

Expressing 870 cc and 1270 cc in terms of the mean and the standard deviation leads to:

$\begin{gathered} 870\text{ cc}=1070\text{ cc }-200\text{ cc}=\mu-\sigma \\ \\ 1270\text{ cc}=1070\text{ cc}+200\text{ cc}=\mu+\sigma \end{gathered}$

Then, this is equivalent to finding the percentage within one standard deviation from the mean. Using the 68-95-99.7 rule, this percentage is:

$\text{ Answer}:68\%$

(b)

From the 68-95-99.7 rule, we know that 99.7% of the data in a normal distribution fall within 3 standard deviations from the mean. Then:

$\begin{gathered} \min\text{ }=1070-3\cdot200=1070-600=470\text{ cc} \\ \max\text{ }=1070+3\cdot200=1070+600=1670\text{ cc} \end{gathered}$

Answer:

Approximately 99.7% of men have cranial capacities between 470 cc and 1670 cc