Question

Suppose that the mean cranial capacity for men is 1190 cc (cubic centimeters) and that the standard deviation is 300 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements. (a) Approximately 68% of men have cranial capacities between | cc and cc. of men have cranial capacities between 590 cc and (b) Approximately 2 1790 cc. 1 x I ?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 1190

standard deviation = $\sigma$ = 300

Using Empirical rule,

a) P( $\mu$ - $\sigma$ < x <  $\mu$ + $\sigma$ ) = 68%

= P( 1190 - 300 < x < 1190 + 300 ) = 68%

= P( 890 < x < 1490 ) =68%

Approximately 68% of men have cranial capacities between 890 cc and 1490 cc

b) P( $\mu$ - 2$\sigma$ < x <  $\mu$ + 2$\sigma$ ) = 95%

= P( 1190 - 2 * 300 < x < 1190 + 2 * 300) = 95%

= P( 1190 - 600 < x < 1190 + 600 ) = 95%

=P( 590 < x < 1790 ) = 95%

Approximately 95% of men have cranial capacities between 590 cc and 1790 cc