The average number of customers per day at a home improvement store is given in the following table. The sine regression equation was found to be y = 33.690sin(0.887x + 1.337) + 81.684, where x represents the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use this model to predict the average number of customers on Thursday. Round to the nearest customer.DaySunMonTueWedThuFriSatNumber of Customers114756051 86118
Thursday is day 5 when counting from Sunday as day 1. Substitute x = 5 into the model: y = 33.690 sin(0.887(5) + 1.337) + 81.684 ≈ 65.2. Rounded to the nearest customer, the prediction is 65 customers, which is choice B.
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