Your parents are always complaining that you do not do enough housework. They say that you should be helping them out because you are only a student and you have a lot more spare time than them. The number of hours per week that your parents work has a mean of 49.24 hours. You know from previous semesters that the number of hours per week that you study for university has a mean of 49.81 hours and a standard deviation of 2.80 hours.

You plan to record the number of hours that you study each week over 18 randomly selected weeks throughout the year. Calculate the probability that the mean of your sample is greater than the mean number of hours per week worked by your parents.

Assume that the population of study hours per week is normally distributed. Give your answer as a decimal to 4 decimal places.