Please answer as fast as possible. Please answer all parts of the question and round answers to three decimal points.

3) In any given year, bad weather can inflict damage to a house. Damages, denoted as Y and expressed in dollars, are randomly distributed, with the following distribution: the probability Y = $1,000 is 80 percent and the probability of Y = $10,000 is 20 percent. = a) Let us assume that 2,000 houses are sufficiently dispersed so that damages to these houses can be viewed as independently distributed random variables, with the above probability distribution. Let denote the average dollar damage calculated from this sample of 2,000 houses. What is the probability that the average damage in any given year exceeds $3,000? Use the normal approximation. b) If the mean that you calculate from the sample of 2,000 observations is equal to $3,000, how many standard deviations is this value from the population mean? c) Assuming the same sample mean and the same number of observations as given in part b), what is the P-value for a two-sided test that the population mean damage is equal to $2,800 versus the alternative that it is not equal to $2,800? Is there evidence to reject the null hypothesis at the 1-percent level of significance? Explain your answer. Would you still reject the null hypothesis if it was a one-sided test (the alternative hypothesis says the population mean is greater than $2,800)? Explain your answer. Use the normal approximation