6) (10) The scores in a statistics exam for Math majors are normally distributed with mean 75 and variance 64. The scores for Engineering majors are also normally distributed with mean 80 and variance 49. The scores are independent. a) If you are a Engineering major, what is the top 10 percentile score in the exam? b) The bottom 15% in the exam (of Math majors) has to retake the course. What is the minimum score required for a student in Math not to retake the course? c) A random sample of 25 Engineering students is taken. What is the probability that the average score is more than 81? d) 60% of the students are Math majors, the remaining are Engineering majors. A random student is selected. What is the probability that her score is higher than 80