Answer-first summary for fast verification
Answer: 0.1056
**Step-by-step solution:** 1. **Given:** X ~ N(3000, 400²) where μ = 3000 and σ = 400 2. **Standardize the value:** We need P(X > 3500) Z = (X - μ)/σ = (3500 - 3000)/400 = 500/400 = 1.25 3. **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.
Author: Nikitesh Somanthe
Ultimate access to all questions.
No comments yet.
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.
A
0.8944
B
0.25
C
0.75
D
0.1056