1. A tax audit team is studying the income tax returns filed in 2020 by people with incomes over $200000. Let p be the fraction of all such tax returns where the total income tax paid, rounded to the nearest whole dollar, was an odd integer. The team takes an initial random sample of 9 of these tax returns, and determines for each of them whether the tax paid was even or odd when rounded; it is found that the number X of tax returns in the sample that yield odd numbers is 2. The team presumes that, wherever the tax payable has been calculated honestly and correctly, it is equally likely to be even or odd when rounded. (a) State the distribution of X. Include the values of parameters. (b) State the team's presumption in the form of a null hypothesis Ho. (c) Assuming Ho is true, calculate P(X =0), P(X = D), and P(X - 2). (d) Test the hypothesis against a two-sided alternative. State both the p-value you obtain and the conclusions you draw