Financial Risk Manager Part 1
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On Tuesday, an insurance company receives a total of 10 claims for automobile policies. After the first-round assessment, it's found that the mean claim amount of the 10 claims is 545 from the list on grounds that it's fraught with fraud. Compute the standard deviation for the remaining set of 9 claims.
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TTanishq
A
110.2
B
12145.2
C
421.8
D
420
Explanation:
Calculation Steps
Step 1: Calculate the total sum of original claims
- Mean = $426, n = 10
- Total sum ∑x = 426 × 10 = 4,260
Step 2: Calculate new total after removing fraudulent claim
- Remove claim of $545
- New ∑x = 4,260 - 545 = 3,715
- New mean = 3,715 ÷ 9 = $412.8
Step 3: Calculate sum of squares for original claims
Using the formula: s² = 1/(n-1)[∑x² - n·x̄²]
- 112² = 1/9[∑x² - 10 × 426²]
- 12,544 = 1/9[∑x² - 1,814,760]
- ∑x² = 12,544 × 9 + 1,814,760 = 1,927,656
Step 4: Calculate sum of squares after removing fraudulent claim
- Remove 545² = 297,025
- New ∑x² = 1,927,656 - 297,025 = 1,630,631
Step 5: Calculate variance for remaining 9 claims
- s² = 1/(9-1)[1,630,631 - 9 × 412.8²]
- s² = 1/8[1,630,631 - 9 × 170,403.84]
- s² = 1/8[1,630,631 - 1,533,634.56]
- s² = 1/8 × 96,996.44 = 12,124.555
Step 6: Calculate standard deviation
- s = √12,124.555 ≈ 110.2
Therefore, the standard deviation for the remaining 9 claims is approximately $110.2
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