7. (a) [5 marks] The length of lectures in 162 are 1 ) The length of lectures in 162 are normally distributed with mean 52 minutes and standard deviation 3 minutes. There are three lectures per week. Write a Matlab script file that uses simulation to estimate the probability that during a week the lecture time exceeds 55 minutes on at least 2 days. (b) (5 marks] Sarah catches the bus to University five days a week. She catches the 211 bus with probability 0.4, the 212 bus with probability 0.5 and the 213 bus with probability 0.1 Write a Matlab script file that uses simulation to estimate probability Sarch catches the 211 bus at least 3 times in a given week. (c) (5 marks] Write a Matlab script file that uses the Monte Carlo method to estimate the integral 2 cos da