Question

Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.

Answer 1

Given;

`\mu=1160,\sigma=200`

The z-score is calculated using;

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \\ z=(760-1160)/(200)\text{ at }x=760 \\ \\ z=-2 \\ \\ z=(1560-1160)/(200)\text{ at }x=1560 \\ \\ z=2 \end{gathered}`

Thus;

`P(-2<strong>ANSWER: </strong><strong>95%</strong><p><strong>(b) </strong>The z-score of 99.7 probability is between -3 and 3. Thus;</p>[tex]\begin{gathered} -3=(x_1-1160)/(200) \\ \\ x_1=560 \\ \\ 3=(x_2-1,160)/(200) \\ \\ x_2=1760 \end{gathered}`

ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc