Let X be the random variable representing the claim amount for flooding damage from house insurance policies of bungalow type houses. Past claims show evidence that X is a normally distributed random variable with an average claim amount of μ = 21000 euro and a standard deviation of σ = 2000 euro, i.e. X~Normal( 21000 , 2000 2). a) Find the z-scores relating to the following claim amounts; i) 25888 : z = (2 dec places) ii) 24779 : z = (2 dec places) iii) 18496 : z = (2 dec places) iv) 23837 : z = (2 dec places) b) Find the probability that for a randomly selected claim, the claim amount will be for less than 25888 euro. (4 dec places) c) Find the probability that for a randomly selected claim, the claim amount will be for more than 24779 euro. (4 dec places) d) Find the probability that for a randomly selected claim, the claim amount will be for between 18496 euro and 23837 euro. (4 dec places) e) An insurance company notes that for 2.5% of claims the claim amount is above K euro, calculate K. (0 dec places)

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Description: Let X be the random variable representing the claim amount for flooding damage from house insurance policies of bungalow type houses. Past claims show evidence that X is a normally distributed random variable with an average claim amount of μ = 21000

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let X be the random variable representing the claim amount for flooding damage from house insurance policies of bungalow type houses. Past claims show evidence that X is a normally distributed random variable with an average claim amount of μ = 21000 euro and a standard deviation of σ = 2000 euro, i.e. X~Normal( 21000 , 2000 ²).

a) Find the z-scores relating to the following claim amounts;
i) 25888 : z = (2 dec places)
ii) 24779 : z = (2 dec places)
iii) 18496 : z = (2 dec places)
iv) 23837 : z = (2 dec places)
b) Find the probability that for a randomly selected claim, the claim amount will be for less than 25888 euro. (4 dec places)
c) Find the probability that for a randomly selected claim, the claim amount will be for more than 24779 euro. (4 dec places)
d) Find the probability that for a randomly selected claim, the claim amount will be for between 18496 euro and 23837 euro. (4 dec places)
e) An insurance company notes that for 2.5% of claims the claim amount is above K euro, calculate K. (0 dec places)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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