An engineer of a company wanted to obtain the Information about the power failures in a small town. He recorded the number of power failures per clay:I for the period of 1D}! consecutive days. He has found that there were 24 clays with no failures. so clays with 1 failure. 31 clays widt I failures, 11 class with 3 failures and 6 stars with 4 or more failures. The data obtained by the engineer are given In the table below. Number of power failures 2 4 or more per air of - - - failures -rda motes... III-- Test at the [tits level of significance whether the number of power failures in the town per day is a random variable hailing Poisson distribution with the lralue of parameter .1 estimated from the sample data. Follow the stem: a. Use sample data to shew that estimated mean of Poisson distribution Is J. = ms [1 outt b. State the hypotheses and the level of significance {1 merit} HI]: H,: c. Calculate the expected frequencies using appropriate row for each calculation. In the expressions for expected frequencies leave two digits after decimal point. [1 market. d. Calculate the value of test statistic using sample data and calculated expected frequencies. (2 marks) bs. e. Determine critical value of the test. (1 mark) Her. f. Determine whether He is rejected and make the conclusions whether the number of power failures in the town per day is a random variable having Poisson distribution with the value of parameter 2 = 1.46. (1 mark)