A manager is attempting to assess the probability of a recession ending in the next six months,and its impact on expected profitability.The manager believes there is a 75 percent chance the recession will end in six months and profits will return to $400 million.However,there is a 25 percent chance the recession will not end in six months,resulting in a $5 million loss.The standard deviation of profits over the next six months is:

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The standard deviation of profits can be calculated using the formula for the standard deviation of a discrete random variable, which involves calculating the expected value (mean) of the profits first and then using the differences from this mean to find the variance and square root of the variance for the standard deviation.Expected profit (mean) = (0.75 * $400 million) + (0.25 * -$5 million) = $300 million - $1.25 million = $298.75 million.Variance = (0.75 * ($400 million - $298.75 million)^2) + (0.25 * (-$5 million - $298.75 million)^2) = (0.75 * $10225 million^2) + (0.25 * $91809.0625 million^2) = $7668.75 million^2 + $22952.265625 million^2 = $30621.015625 million^2.Standard deviation = sqrt($30621.015625 million^2) ≈ $175.0 million.The calculation involves finding the expected value, calculating the squared differences from this expected value, finding the weighted sum of these squared differences (variance), and then taking the square root of the variance to get the standard deviation. The closest answer provided is $175.37 million, which is a slight approximation difference.

A Manager Is Attempting to Assess the Probability of a Recession