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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) b) (2 marks) (Do by hand) In Lesson 1 of Week 8 we introduced the Central Limit theorem. Formally, it states: \"Let X1, X 2, ..., Xn be 11 independent and identically distributed random variables from a population with mean u and standard deviation 0' Then provided that n is sufciently large _ 02 \"(M 7) Under most conditions suz'ciently 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. (1 mark) (Do by hand) Consider the random sample of 40 bus times drawn, solve for P(_X