Based on information from the National Center for Health Statistics, the heights of 10-year-old girls closely follow a Normal distribution with mean 54.5 inches and standard deviation 2.7 inches. The heights of 10-year-old boys follow a Normal distribution with mean 54.1 inches and standard deviation 2.4 inches. A particular fourth-grade class has 10 girls and 7 boys. The children's heights are recorded on their tenth birthdays. (a) Treat the students in this class as random samples of 10-year-old boys and girls. Use random variables to calculate the probability that the mean height of the girls is greater than the mean height of the boys. Show your work.