Financial Risk Manager Part 1
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After 72 FRM Part 1 students took a mock exam, the mean score was 75. Assuming that the population standard deviation is 10, construct a 99% confidence interval for the mean score on the mock exam.
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Community
NNikitesh
A
(75, 85)
B
(65, 75)
C
(71.96, 78.04)
D
(75, 78.04)
Explanation:
A 99% confidence interval for the mean is calculated using the formula: μ = x̄ ± Zα/2 * σ/√n where α = 0.01
From the normal distribution table, Z₀.₀₀₅ = 2.58
Given:
- Sample mean (x̄) = 75
- Population standard deviation (σ) = 10
- Sample size (n) = 72
Calculation: μ = 75 ± 2.58 * 10/√72 = 75 ± 2.58 * 10/8.4853 = 75 ± 2.58 * 1.1785 = 75 ± 3.04
Therefore, the 99% confidence interval is: 71.96 ≤ μ ≤ 78.04
This means we can be 99% confident that the true population mean score lies between 71.96 and 78.04.
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