Question

suppose that the mean cranial capacity for men is 1180 cc (cubic centimeters) and that the standard deviation is 300 cc. assuming that mens cranial capacities are normally distributed, complete the following statements. (a) approximately? of men have cranial capacities between 880 cc and 1480 cc. (b) approximately 68% 75% 95% 99.7% men have cranial capacities between cc and cc.

Explanation:

Step1: Calculate z - scores for part (a)

For $x_1 = 880$, $z_1=\frac{880 - 1180}{300}=\frac{- 300}{300}=-1$. For $x_2 = 1480$, $z_2=\frac{1480 - 1180}{300}=\frac{300}{300}=1$. According to the empirical rule of normal - distribution, approximately 68% of the data lies within 1 standard deviation of the mean.

Step2: For part (b) with 95% confidence

According to the empirical rule of normal - distribution, approximately 95% of the data lies within 2 standard deviations of the mean. The lower bound is $\mu-2\sigma=1180 - 2\times300=1180 - 600 = 580$ cc. The upper bound is $\mu + 2\sigma=1180+2\times300=1180 + 600 = 1780$ cc.

Answer:

(a) 68%
(b) 580 cc, 1780 cc