The margin of error of the 99.7% confidence interval is
[tex]ME=0.566-0.5=0.5-0.434=0.066[/tex]
This computed margin or error is actually 3 standard deviations from the mean according to the empirical rule. The empirical rule states that 3 standard deviations away from the mean constitute the 99.7%.
Therefore, the value 0.066 is 3 times the standard deviation. The standard deviation, SE, is
[tex]SE=0.066\div 3=0.022[/tex]
The standard deviation is 0.022.
