Financial Risk Manager Part 1
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Insurance claims in a certain class of business are modeled using a normal distribution with mean $3,000 and a standard deviation of $400. Calculate the probability that the next claim received will exceed $3,500. Please click here to view the standard normal table
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TTanishq
A
0.8944
B
0.25
C
0.75
D
0.1056
Explanation:
Explanation
Given:
- X ~ N(3000, 400²) - Normal distribution with mean μ = 3000 and standard deviation σ = 400
- We need to find P(X > 3500)
Step 1: Standardize the variable
Step 2: Find the probability
Step 3: Use the standard normal table From the standard normal table:
- P(Z < 1.25) = 0.8944
- Therefore: P(Z > 1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056
Verification:
- The standard normal distribution is symmetric
- About 68% of values lie within ±1 standard deviation
- About 95% of values lie within ±2 standard deviations
- Since 3500 is 1.25 standard deviations above the mean, the probability of exceeding this value should be relatively small, which matches our calculated result of 0.1056 (about 10.56%).
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