Solve the below problem:
Q: An article in the Journal of Cardiovascular Magnetic Resonance ["Right Ventricular Ejection Fraction Is Better Reflected by Transverse Rather Than Longitudinal Wall Motion in Pulmonary Hypertension" (2010, Vol.12(35)] discussed a study of the regional right ventricle transverse wall motion inpatients with pulmonary hypertension (PH). The right ventricle ejection fraction (EF) was approximately normally distributed with a mean and a standard deviation of 36 and 12, respectively,for PH subjects, and with mean and standard deviation of 56 and 8, respectively, for control subjects.
(a) What is the EF for PH subjects exceeded with 5% probability?
(b) What is the probability that the EF of a control subject is less than the value in part (a)?
(c) Comment on how well the control and PH subjects can be distinguished by EF measurements.