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 47.84 hours and a standard deviation of 2.25 hours. You believe that the number of hours per week that you have to study for university has a mean of 47.91 hours and a standard deviation of 2.48 hours.

You plan to record the number of hours that you study each week over 19 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. You may find thisstandard normal tableuseful. Give your answer as a decimal to 4 decimal places.