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A salesman for energy-efficient radiant barrier attic insulation believes a home

ID: 3058381 • Letter: A

Question

A salesman for energy-efficient radiant barrier attic insulation believes a homeowner with a newer roof is more likely to purchase his product. Looking over past records of sales agents soliciting businesses by ringing doorbells and discussing their products, he sorts the sales records into three groups: customers with a 30-year roof in good condition, those with a 20-year roof in good condition, and those in need of a new roof. His results are in the following table.

Does knowing the condition of a prospective customer's roof help the salesman determine who is a more likely candidate for an insulation sale? What would you advise a door-to-door salesman of the radiant barrier insulation? Why? Justify your answer using appropriate probabilities and the concept of independence.

30-year roof 20-year roof in need of a New Roof total Purchased insulation 8 5 4 17 Did not make a purchase 42 77 94 213 Total 50 82 98 230

Explanation / Answer

A salesman for energy-efficient radiant barrier attic insulation believes a homeowner with a newer roof is more likely to purchase his product. Looking over past records of sales agents soliciting businesses by ringing doorbells and discussing their products, he sorts the sales records into three groups: customers with a 30-year roof in good condition, those with a 20-year roof in good condition, and those in need of a new roof. His results are in the following table.

Does knowing the condition of a prospective customer's roof help the salesman determine who is a more likely candidate for an insulation sale? What would you advise a door-to-door salesman of the radiant barrier insulation? Why? Justify your answer using appropriate probabilities and the concept of independence.

30-year roof 20-year roof in need of a New Roof total Purchased insulation 8 5 4 17 Did not make a purchase 42 77 94 213 Total 50 82 98 230
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