According to a hypothetical study, the mean age of women who are diagnosed as having breast cancer in Philadelphia is 35, with standard deviation 7. If the ages of women are normally distributed, suppose that we randomly sample 49 women from Philly who are diagnosed as having breast cancer.

a. What is the distribution of the mean age of those 49 women? (10 points)

In other words, X ( , )

b. What is the z score such that 29.46% of the women fall below that z? Sketch the graph of the curve and shade the area. (10 points)

c. What is the mean age for women corresponding to the z score you found in part b? Show your work to receive full credit. (10 points)