Question 1 (3 marks) Please scroll to the bottom of page for END of question. A study reveals that the number of goals per match in the world cup can be approximated by a Poisson distribution, with a mean of 2.5. (a) Find the probability of 4 goals in a match (4 decimals). (1 mark) Answer: (b) If there have been already two goals in a match, what is the probability that there are four goals at the end of the match (4 decimals)? (1 mark) Answer: (c) If there are already two goals in a match, what is the probability that there are at least four goals at the end of the match (4 decimals)? (1 mark) Answer:Using the g(x) in part (c) and the stopping (d) criterion obtained in part (b), carry out the iteration scheme Intl = 9(In), with To = 0. Find an approximate solution of (2 marks) f(z) = 0, & E [0, 1] that is correct to 3 decimal places. n = (integer input) Xn = (3 decimals) Question 3 (6 marks) Please scroll to the bottom of page for END of question. A recent survey reveals that the average monthly wage (in SGD) in Singapore is 4789. A sample of size 61 is selected from some community, and it is found that the sample mean is 5421 with a standard deviation of 830. Using a significance level of 1%, determine whether the community on average earns a higher level of monthly wage than the national average. (a) Let X be the monthly wage of a person in the given community. What is the parameter of interest? (1 mark) Please choose one: a) Sample mean, X b) Sample variance, $2 c) Mean of X, H d) Variance of X, 2Question 2 (8 marks) Please scroll to the bottom of page for END of question. Use fixed-point iteration method to solve f(I) = 13 - 72 + 2 =0, x 6 [0, 1]. Your approximate solution should be correct up to 3 decimal places. (a) Does the interval [0, 1] contain a root of f(z) = 0? (1 mark) Please choose one: a) O No bJO Yes Set up a stopping criterion as follows (b) absolute error = [In - I'Is If ( In )I