Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. The following histogram shows the distribution of house values in a certain city. The mean ofthe distribution is $403,000 and the standard deviation is $278,000. (a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work. (b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work. 0.40 0.30 0.25-l 0.20 0.15- 0.-%10 0.05 CI' Relative Frequency 0 500 1.000 1 .500 2,000 2.500 Value (thousands of dollars)