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For Company A there is a 60% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $9,000 and standard deviation $2,000. Assume that the total claim amounts of the two companies are independent. What is the probability that in the coming vear Company R's total claim amount will

For Company A there is a 60% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $9,000 and standard deviation $2,000. Assume that the total claim amounts of the two companies are independent. What is the probability that in the coming vear Company R's total claim amount will

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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For Company A there is a 60% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $9,000 and standard deviation $2,000. Assume that the total claim amounts of the two companies are independent. What is the probability that, in the coming year, Company B's total claim amount will exceed Company A's total claim amount? Let X be a continuous random variable with density function (2x, x22 Ax) =; 0, otherwise 1 for 0<y<1. X-1 Determine the probability density function of Y =: Claim amounts at an insurance company are independent of one another. In year one, claim amounts are modeled by a normal random variable X with mean 100 and standard deviation 25. In year two, claim amounts are modeled by the random variable Y = 1.04X + 5. Calculate the probability that a random sample of 25 claim amounts in year two has an average between 100 and 110.
Transcribed Image Text:For Company A there is a 60% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $9,000 and standard deviation $2,000. Assume that the total claim amounts of the two companies are independent. What is the probability that, in the coming year, Company B's total claim amount will exceed Company A's total claim amount? Let X be a continuous random variable with density function (2x, x22 Ax) =; 0, otherwise 1 for 0<y<1. X-1 Determine the probability density function of Y =: Claim amounts at an insurance company are independent of one another. In year one, claim amounts are modeled by a normal random variable X with mean 100 and standard deviation 25. In year two, claim amounts are modeled by the random variable Y = 1.04X + 5. Calculate the probability that a random sample of 25 claim amounts in year two has an average between 100 and 110.
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