Calculate how much needs to be invested in a no-load mutual fund that yields 5% if $28,750 is needed each year. (Round your answer to the nearest whole number.) Investment amount $

Please answer questions

Find the present value of the investment. (Round your answer to the nearest cent.) worth $13,000 after 2.5 years at 5.25% simple annual interest 14706.25 X

An insurance company believes that claim amounts in a certain portfolio of policies follow a normal distribution. An analyst chose 61 policies at random which gave a sample mean of K5,230 and a sample standard deviation of K810.(a) Construct a 95% confidence interval for the mean claim amount in the portfolio. (3)(b) The company has changed its loss assessment processes in order to reduce claim sizes on average, targeting a reduction of K200 compared to the current mean. It does not expect a change to the variability of claim amounts. The company in- tends to verify whether the target has been met by using a sample of claims to test the null hypothesis that there is no change, against a one-sided alternative hy- pothesis. Company policy is to perform statistical tests at a significance level of 5%.8. (a)Determine the smallest number of claims that would need to be sampled underthe new processes for a K200 reduction to be statistically significant in the test.