Question 5. A insurance company have a doubt on the average losses made in their new promoted policy. An actuary was assigned to investigate this new policy. The actuary was originally told that the average losses made in this new policy is $0.2$ millions and the variance of the losses of this new policy is $1.21$ millions. a) Suppose the actuary also given 10,000 samples where each sample has a sample size of 16. The actuary first construct a distribution of the sample means based on the given samples and obtain the mean and standard deviation for the sample mean. Please state, with reasons, the distribution of sample mean. b) (2 mark Calculate the mean and the standard deviation of the sample mean mentioned in part a). C) ) Then, the actuary was told that the provided samples are mixed together with other dataset and only the sample in the Table below can be trusted -1.3220 -0.0639 -1.0179 -0.8416 -0.7502 -0.9540 -0.6623 -2.4018 -0.2313 -0.0373 0.3522 0.6685 0.6713 -0.7486 1.1059 1.5690 Perform a hypothesis testing on the population mean a = 0.2. where the significance level B = 0.05 (please note that in the above sample a positive figure refers a loss made on a policy while a negative figure refers to profit made on a policy