Question

The Army reports that the distribution of head circumference among male soldiers is approximately normal with mean 22 and standard deviation 0.9. Use the Empirical Rule to answer the following questions.

The Army reports that the distribution of head circumference among male soldiers is approximately normal with mean 22 and standard deviation 0.9. Use the Empirical Rule to answer the following questions What percent of soldiers have head circumferences greater than 22.9? What percent of soldiers have head circumferences between 21.1 and 22.92

Answer 1

Solution :

Given that,

$\mu$ = 22

$\sigma$ = 0.9

Using Empirical rule,

(a)

P ( x > 22.9 ) = 16%

(b)

P($\mu$ - 1$\sigma$< X < $\mu$ + 1$\sigma$) = 68%

P( 22  - 0.90 < X < 22 + 0.90) = 68%

P( 21.1 < X < 22.90) = 68%

  68 %