(a) Discuss briefly the impact of Central Limit Theorem on sampling distribution of mean. (b) Discuss briefly sampling distribution. (c) The management of a large national chain of hotels decided to estimate the mean cost per room of repairing damages made by its customers during a weekend. A random sample of 100 vacated rooms was inspected by the management. Its analysis estimated the mean repair cost to be RM25 and the sample standard deviation to be RM10. (i) Construct a 95% confidence interval for the mean repair cost, , of all its rooms. Interpret your answer. (ii) Construct a 99% confidence interval for the mean repair cost, , of all its rooms. Interpret your answer. (iii) Without showing the working, when the sample size is increased, state if the confidence interval will be wider or narrower. (iv) Without showing the working, when the standard deviation increased, state if the confidence interval will be wider or narrower. (v) Without showing the working, when the mean increased, state if the confidence interval will be wider or narrower