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A retailer classifies accounts as having one of four possible states: "paid up." "overdue at most 30 days," "overdue less than 60 days but more than 30 days," and "bad." If no payment is made on an overdue account by the end of the month, the status moves to the next state. When a partial payment is Paid 1 made on an overdue account, its improved status depends on the size of the payment. The matrix on the right describes the changes in status of accounts. Paid s30 <60 Bad 0.3 0.2 0 s 30 0 0.2 0.2 < 60 0 0.5 0.4 Bad 0 0.2 1 (a) What is the probability of an account eventually being paid off f it is currently overdue at most 30 days? |Currently overdue Probability At most 30 days What is the probability of an account eventually being paid off if it is currently overdue less than 60 days? Currently overdue Less than 60 days Probability (b) If an account is currently overdue at most 30 days, what is the expected number of months until it is either paid or bad? months (c) If the company has $3000 in bills in the "s 30 days" category and 8000 in bills in the "< 60 days" category, how much can the retailer expect will eventuall paid up and how much will eventually be irretrievable bad debt? Will eventually be paid up debt Will eventually be irretrievable bad debt (Round to the nearest dollar as needed.)

A retailer classifies accounts as having one of four possible states: "paid up." "overdue at most 30 days," "overdue less than 60 days but more than 30 days," and "bad." If no payment is made on an overdue account by the end of the month, the status moves to the next state. When a partial payment is Paid 1 made on an overdue account, its improved status depends on the size of the payment. The matrix on the right describes the changes in status of accounts. Paid s30 <60 Bad 0.3 0.2 0 s 30 0 0.2 0.2 < 60 0 0.5 0.4 Bad 0 0.2 1 (a) What is the probability of an account eventually being paid off f it is currently overdue at most 30 days? |Currently overdue Probability At most 30 days What is the probability of an account eventually being paid off if it is currently overdue less than 60 days? Currently overdue Less than 60 days Probability (b) If an account is currently overdue at most 30 days, what is the expected number of months until it is either paid or bad? months (c) If the company has $3000 in bills in the "s 30 days" category and 8000 in bills in the "< 60 days" category, how much can the retailer expect will eventuall paid up and how much will eventually be irretrievable bad debt? Will eventually be paid up debt Will eventually be irretrievable bad debt (Round to the nearest dollar as needed.)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter11: Matrices And Determinants
Section11.CR: Chapter Review
Problem 2CC: What is the row-echelon form of a matrix? What is a leading entry?
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A retailer classifies accounts as having one of four possible states: "paid up," "overdue at most 30 days," "overdue less than 60 days but more than 30 days," and "bad." If no payment is made on an overdue account by the end of the month, the status moves to the next state. When a partial payment is Paid made on an overdue account, its improved status depends on the size of the payment. The matrix on the right describes the changes in status of accounts. Paid s30 < 60 Bad 0.3 0.2 <30 0.2 0.2 < 60 0.5 0.4 Bad 0.2 1 ... (a) What is the probability of an account eventually being paid off if it is currently overdue at most 30 days? Currently overdue Probability At most 30 days What is the probability of an account eventually being paid off if it is currently overdue less than 60 days? Currently overdue Probability Less than 60 days (b) lf an account is currently overdue at most 30 days, what is the expected number of months until it is either paid or bad? months (c) If the company has $3000 in bills in the "s 30 days" category and $8000 in bills in the "< 60 days" category, how much can the retailer expect will eventually be paid up and how much will eventually be irretrievable bad debt? Will eventually be paid up debt Will eventually be irretrievable bad debt (Round to the nearest dollar as needed.)
Transcribed Image Text:A retailer classifies accounts as having one of four possible states: "paid up," "overdue at most 30 days," "overdue less than 60 days but more than 30 days," and "bad." If no payment is made on an overdue account by the end of the month, the status moves to the next state. When a partial payment is Paid made on an overdue account, its improved status depends on the size of the payment. The matrix on the right describes the changes in status of accounts. Paid s30 < 60 Bad 0.3 0.2 <30 0.2 0.2 < 60 0.5 0.4 Bad 0.2 1 ... (a) What is the probability of an account eventually being paid off if it is currently overdue at most 30 days? Currently overdue Probability At most 30 days What is the probability of an account eventually being paid off if it is currently overdue less than 60 days? Currently overdue Probability Less than 60 days (b) lf an account is currently overdue at most 30 days, what is the expected number of months until it is either paid or bad? months (c) If the company has $3000 in bills in the "s 30 days" category and $8000 in bills in the "< 60 days" category, how much can the retailer expect will eventually be paid up and how much will eventually be irretrievable bad debt? Will eventually be paid up debt Will eventually be irretrievable bad debt (Round to the nearest dollar as needed.)
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