Can someone help me out to solve this problem? Because I get stuck on part a, I can continue rest of them. I know it is something like y= g(x), but my answer is really weird number for a 1/sqrt(2pi*9)e^-(e^y/(1+e^y) - 5)^2 / (9^2)*2 * ( e^y/(1+e^y)^2) which looks incorrect.

4. Assume the log odds of the final scores (in percentage) of a course at UBC are normally distributed with mean 5 and standard deviation 9. There are 100 students in total. Suppose that whether a student passes the course (i.e., the final score (in percentage) is greater than or equal to 50%) or not is independent from other students. Note: The log odds is defined as Y = log _ _, where X represents the final score in percentage of a randomly chosen UBC student. Here, we refer to log as the natural logarithm. For the following questions, round your final answers to 3 decimal places. (a) Find the probability density function of the final scores (in percentage). (b) What is the probability that a randomly selected student passes the course? (c) Find the expectation and variance of the number of students that pass the course. (d) Find the approximate probability that no less than 70 students pass the course. State and verify the conditions that you use for the approximation if there are any