Left-handedness is a trait that is found in about 11 % of the general population. Past studies have shown that left-handed men are overrepresented among professional boxers. To investigate this theory, a random sample of 500 professional male boxers was surveyed, and it was found that 81 were left-handed while the other 419 were right-handed.
Since we do not know the proportion of all professional male boxers who are left-handed, we need to estimate the standard deviation of the sampling distribution of the sample proportion with the standard error. Use the observed data to calculate the standard error of the sample proportion. Round to the nearest ten-thousandth.