Lowe's sells a very popular remote control operated ceiling fan, the Lantern Bay 54-in Matte Black LED Indoor/Outdoor Ceiling fan, with most of the sales being made in the summer months. Lowes makes a one-time purchase of these fans prior to each summer season at a cost of $40 each and sells each Lantern Bay fan for $200. Any fans unsold at the end of the summer season are marked down to $50 and sold in a special fall sale. By experience, all marked-down fans are sold. The following is the number of Lantern Bay fans sold during the last past 10 summers: 30, 50, 30, 60, 10, 40, 30, 30, 20, 40. 1. Estimate the mean and the variance of the demand for Lantern Bay fans each summer. 2. Assume that the demand for Lantern Bay fans each summer follow a normal distribution, with mean and variance gi

gaby131o

gaby131o

Answered question

2022-09-24

Lowe's sells a very popular remote control operated ceiling fan, the Lantern Bay 54-in Matte Black LED Indoor/Outdoor Ceiling fan, with most of the sales being made in the summer months. Lowes makes a one-time purchase of these fans prior to each summer season at a cost of $40 each and sells each Lantern Bay fan for $200. Any fans unsold at the end of the summer season are marked down to $50 and sold in a special fall sale. By experience, all marked-down fans are sold. The following is the number of Lantern Bay fans sold during the last past 10 summers: 30 , 50 , 30 , 60 , 10 , 40 , 30 , 30 , 20 , 40.
1. Estimate the mean and the variance of the demand for Lantern Bay fans each summer.
2. Assume that the demand for Lantern Bay fans each summer follow a normal distribution, with mean and variance given by your answer on 1). Determine the optimal number of fans for Lowes to buy prior to each summer season.

Answer & Explanation

Laylah Bean

Laylah Bean

Beginner2022-09-25Added 4 answers

Demand for fans, during last 10 summers 30 , 50 , 30 , 60 , 10 , 40 , 30 , 30 , 20 , 40.
Mean ( x ¯ ) = sum of all abservation  total number of observation = 30 + 50 + 30 + 60 + 10 + 40 + 30 + 30 + 20 + 40 10
Mean ( x ¯ ) = 340 10 = 34
Variance = 1 N 1 L 1 N ( x 2 x ¯ ) 2
Variance = ( 30 34 ) 2 + ( 50 34 ) 2 + + ( 40 34 ) 2 10 1
Variance = 204.4444

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