Explanation:
When four times the number of scenarios are generated, the range of the 95% confidence interval will be cut in half. Thus, a quick calculation is to just divide the $2.97 distance from the mean from the 100 scenario run by two then add and subtract this distance from the mean of $120. Alternatively, the following two formulas show how the old and new confidence intervals are determined:
Old 95% CI:
\left(\`$120` - 1.98 \times \frac{\`$15`}{\sqrt{100}},\ \`$120` + 1.98 \times \frac{\`$15`}{\sqrt{100}}\right) = \`$120` \pm 2.97 = (\`$117.03`,\ \`$122.97`)New 95% CI:
\left(\`$120` - 1.98 \times \frac{\`$15`}{\sqrt{400}},\ \`$120` + 1.98 \times \frac{\`$15`}{\sqrt{400}}\right) = \`$120` \pm 1.47 = (\`$118.53`,\ \`$121.47`)(Book 2, Module 24.1, LO 24.b)
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Question 100
The 95% confidence interval for the output of ending capital is calculated to be ($117.03, $122.97) for a simulation run with 100 scenarios. In addition, the simulation resulted in a mean-ending capital amount of $120 with a standard deviation of $15. Suppose you want to improve the accuracy of this confidence interval by running a simulation of 400 scenarios. What is the new 95% confidence interval with a simulation of 400 scenarios using the same mean and standard deviations from the model with 100 scenarios?
A
($117.23, $122.95).
B
($118.53, $121.47).
C
($119.02, $121.99).
D
($119.71, $122.27).
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