Answer
approximate 75% of the population fall in [148,312] when k = 2
approximate 84% of the population fall in [127.5,332.5] when k=2.5
approximate 89% of the population fall in [107,353] when k = 3
Work Step by Step
Interval:
x`+-2s = 230 +- 2(41) = [148,312]
x`+-2.5s = 230 +- 2.5(41) = [127.5,332.5]
x`+-2.5s = 230 +- 3(41) = [107,353]
Percentage Population:
$1-1/k^2 $
$k=2 , 1-1/4 = 3/4 *100 = 75%$
$k=2.5 , 1-1/2.5^2 = 21/25 * 100 = 84%$
$k=3 , 1-1/3^2 = 8/9 * 100 = 89%$
