Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
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.
Other
Community
NNikitesh
A
0.8944
B
0.25
C
0.75
D
0.1056
Explanation:
Step-by-step solution:
-
Given: X ~ N(3000, 400²) where μ = 3000 and σ = 400
-
Standardize the value: We need P(X > 3500)
Z = (X - μ)/σ = (3500 - 3000)/400 = 500/400 = 1.25
-
Find the probability: P(X > 3500) = P(Z > 1.25)
Using the standard normal distribution table: P(Z < 1.25) = 0.8944
Therefore: P(Z > 1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056
Interpretation: There's approximately a 10.56% probability that the next claim will exceed $3,500.
Key concept: This is a standard normal distribution problem where we convert the raw score to a z-score and use the standard normal distribution table to find probabilities.
Comments
Loading comments...