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Martin will be renovating her store, Avenew. He is concerned that his business is growing too fast, and that his facility needs to catch up with customer needs. Using the data that she collected from all his previous customer, he was able to conclude that the weight of rectangular tables is normally distributed with a mean of 28 kg and a variance of 11 kg?. The weight of circular tables, on the other hand, follow a uniform distribution with bounds of 16 kg and 24 kg. He was also able to conclude that the weight of the square table customers is normally distributed with a mean of 23 kg and a variance of 18 kg². a. What is the probability that a random circular table weighs within 2 kg of the average square table? b. What is the probability that a random rectangular table weighs more than the average circular table? c. What is the probability that a random square table weighs more than the average circular table but less than the weight where 50% of all rectangular tables fall? d. Tables are sent to the deluxe room if they weigh less than 20 kg, to the premium room if they weigh more than 20 kg but less than 25 kg, and to the executive lounge

Martin will be renovating her store, Avenew. He is concerned that his business is growing too fast, and that his facility needs to catch up with customer needs. Using the data that she collected from all his previous customer, he was able to conclude that the weight of rectangular tables is normally distributed with a mean of 28 kg and a variance of 11 kg?. The weight of circular tables, on the other hand, follow a uniform distribution with bounds of 16 kg and 24 kg. He was also able to conclude that the weight of the square table customers is normally distributed with a mean of 23 kg and a variance of 18 kg². a. What is the probability that a random circular table weighs within 2 kg of the average square table? b. What is the probability that a random rectangular table weighs more than the average circular table? c. What is the probability that a random square table weighs more than the average circular table but less than the weight where 50% of all rectangular tables fall? d. Tables are sent to the deluxe room if they weigh less than 20 kg, to the premium room if they weigh more than 20 kg but less than 25 kg, and to the executive lounge

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Martin will be renovating her store, Avenew. He is concerned that his business is growing too fast, and that his facility needs to catch up with customer needs. Using the data that she collected from all his previous customer, he was able to conclude that the weight of rectangular tables is normally distributed with a mean of 28 kg and a variance of 11 kg?. The weight of circular tables, on the other hand, follow a uniform distribution with bounds of 16 kg and 24 kg. He was also able to conclude that the weight of the square table customers is normally distributed with a mean of 23 kg and a variance of 18 kg?. a. What is the probability that a random circular table weighs within 2 kg of the average square table? b. What is the probability that a random rectangular table weighs more than the average circular table? c. What is the probability that a random square table weighs more than the average circular table but less than the weight where 50% of all rectangular tables fall? d. Tables are sent to the deluxe room if they weigh less than 20 kg, to the premium room if they weigh more than 20 kg but less than 25 kg, and to the executive lounge if they weigh more than 25 kg. If, on average, Avenew receives 10 rectangular tables, 12 circular tables and 8 square tables daily, and there is a one table per room policy, how many rooms of each type should Martin prepare to ensure that all tables have a room at any given day?
Transcribed Image Text:Martin will be renovating her store, Avenew. He is concerned that his business is growing too fast, and that his facility needs to catch up with customer needs. Using the data that she collected from all his previous customer, he was able to conclude that the weight of rectangular tables is normally distributed with a mean of 28 kg and a variance of 11 kg?. The weight of circular tables, on the other hand, follow a uniform distribution with bounds of 16 kg and 24 kg. He was also able to conclude that the weight of the square table customers is normally distributed with a mean of 23 kg and a variance of 18 kg?. a. What is the probability that a random circular table weighs within 2 kg of the average square table? b. What is the probability that a random rectangular table weighs more than the average circular table? c. What is the probability that a random square table weighs more than the average circular table but less than the weight where 50% of all rectangular tables fall? d. Tables are sent to the deluxe room if they weigh less than 20 kg, to the premium room if they weigh more than 20 kg but less than 25 kg, and to the executive lounge if they weigh more than 25 kg. If, on average, Avenew receives 10 rectangular tables, 12 circular tables and 8 square tables daily, and there is a one table per room policy, how many rooms of each type should Martin prepare to ensure that all tables have a room at any given day?
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