In area A the selling price of homes has a normal distribution with mean PA =130 thousand and a standard deviation of VA = 20 thousand, while in area B the selling price of homes had a normal distribution with mean PB = 150 and standard deviation of Vb = 25 thousand. a. Suppose that n = 30 homes are selected at random from Area B. i. (1 mark) Find the sampling distribution of the sample mean. ii. (3 marks) Find the probability that the sample mean is between 157 thousand and 164 thousand. iii. (2 marks) Find the probability that the sample mean is at least 155 thousand. iv. (2 marks) Find the probability that the sample mean is at most 165 thousand. b. Suppose that n = 100 homes are selected at random from Area B. i. (1 mark) Find the sampling distribution of the sample mean. ii. (3 marks) Find the probability that the sample mean is between 157 thousand and 164 thousand. iii. (2 marks) Find the probability that the sample mean is at least 155 thousand