Please refer to the following iamge

Question 1: (15 marks) Waiting for a bus is modeled as a continuous Uniform random variable that can take on any value between 0 to 20 minutes. Let X= waiting time for a bus, hence X~ Unif(0,20). a) (2 marks) (Do by hand) In Lesson 1 of Week 8 we introduced the Central Limit theorem. Formally, it states: "Let X1, X2, ... Xn be n independent and identically distributed random variables from a population with mean / and standard deviation o Then provided that n is sufficiently large X~N H, n Under most conditions sufficiently large is for n>30" Consider our current population modeled as X~Unif(0, 20). If we draw a random sample of size 40 units from this population state the distribution of X = average waiting time for a sample of size 40. b) (1 mark) (Do by hand) Consider the random sample of 40 bus times drawn, solve for P(X