The marginal loss on Washington reds, a brand of apples from the state of Washington, is $35 per case. The marginal profit is $15 per case. During the past year, the mean sales of Washington Reds in cases was 45,000 cases, and the standard deviation was 4,450. How many cases of Washington Reds should be brought to market? Assume that sales follows a normal distribution.

Question

Tito

Mathematics

20 December, 05:01

The marginal loss on Washington reds, a brand of apples from the state of Washington, is $35 per case. The marginal profit is $15 per case. During the past year, the mean sales of Washington Reds in cases was 45,000 cases, and the standard deviation was 4,450. How many cases of Washington Reds should be brought to market? Assume that sales follows a normal distribution.

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Camden Hurst · Answer 1

42666 cases

Step-by-step explanation:

P = (Marginal Loss) / (Marginal Loss + Marginal Profit)

P = (35) / (35+15) = 0.7

Considering a normal distribution we can find the corresponding z value by P = 0.7 (which represented the shaded area under the curve)

z = 0.5244

z = (X - Mean Sales) / Standard Deviation

-0.5244 = (X - 45000) / 4450

X = 42666.42 ≅ 42666