1. (a) Explain the purpose of the COUNTIF function in Excel and give a business example for which this function would be a useful tool for analysis. (6 marks) (b) You are embarking on a risky business project for which there are three possible outcomes: (A) a loss of 20,000, (B) break even, i.e. a payoff of 0, and (C) a profit of 70,000. Outcome (A) is two-thirds the probability of outcome (B). Outcome (C) is twice as likely as outcome (A). i. Determine the numerical probabilities for outcomes A, B and C, reporting each in its simplest fractional form. (4 marks) ii. Calculate the expected outcome from this risky business project. (3 marks) iii. Calculate the standard deviation from this risky business project. (4 marks) (c) Each year 3.4% of all tax returns are audited. In a batch of 150 tax returns, of interest is the probability that at most two tax returns are audited. A spreadsheet model of this problem is: A B E 1 Auditing tax returns D Data table 2 n P(