Question

what is the expected value if the annual budget is $279,740,088 and the percentage spent is 8.33% and what is the variance if the actual spent was $23,500,000?

Answer 1

What is the expected value if the annual budget is $279,740,088 and the percentage spent is 8.33% and what is the variance if the actual spent was $23,500,000?

Solution

Find

The expected spent = The annual budget * The percentage spent = ($279,740,088 * 8.33%)/100% = $23,302,349

The variance of a variable is the expected value of the squared deviation from the mean $\bar{x}$

$$\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$$

The variance = $\sigma^2 = \frac{(\text{The expected spent} - \bar{x})^2 + (\text{The actual spent} - \bar{x})^2}{n}$

$$\bar{x} = \frac{\text{The expected spent} + \text{The actual spent}}{2} = \$23,401,175$$ $$\sigma^2 = \frac{(\$23,302,349 - \$23,401,175)^2 + (\$23,500,000 - \$23,401,175)^2}{2} = \frac{9,766,578,276 + 9,766,380,625}{2} = 9,766,479,451$$

Answer: The expected spent = $23,302,349; The variance = 9,766,479,451