Question

suppose that the mean cranial capacity for men is 1180 cc (cubic centimeters) and that the standard deviation is 300 cc. assuming that are normally distributed, complete the following statements. (a) approximately 68% of men have cranial capacities between 880 cc and 1480 cc. (b) approximately 99.7% of men have cranial capacities between cc and cc.

Explanation:

Step1: Recall empirical rule for normal distribution

For a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean. Let the mean be $\mu = 1180$ cc and the standard deviation be $\sigma=300$ cc.
The lower bound is $\mu-\sigma$ and the upper bound is $\mu + \sigma$.
$\mu-\sigma=1180 - 300=880$ cc and $\mu+\sigma=1180 + 300 = 1480$ cc.

Step2: Recall 99.7% rule for normal distribution

About 99.7% of the data lies within 3 standard deviations of the mean. The lower bound is $\mu - 3\sigma$ and the upper bound is $\mu+3\sigma$.
$\mu - 3\sigma=1180-3\times300=1180 - 900 = 280$ cc and $\mu+3\sigma=1180 + 3\times300=1180+900 = 2080$ cc.

Answer:

(a) 1480
(b) 280, 2080