Data was collected on reaction time of both hands for an experiment. 14 out of 27 students had a faster reaction time with their right hand than with their left hand. Using this information, we wish to construct a confidence interval for the proportion of all WCU students that have a faster reaction time with their right hand than with their left hand. Calculate the upper boundary of a 99% confidence interval.

Give your answer as a decimal rounded to 3 places after the decimal.