You have been asked to determine the probability that the contribution margin fo

Question

You have been asked to determine the probability that the contribution margin for a particular product line exceeds the xed cost of 3620 The total mbr random variable with a mean of 400 and a variance of 900 x -N(400, 900) The selling price per unit is $12 The total nmber of un produced nomalily uedvriable with mean of 400 and a variance of 1600 Y-N(400, 1600). The variable production cost is $4 per unit Production and sales have a potive com of 5 What is the probability that the contribution margin for the product line exceeds the fixed cost of s3620 (Type an integer or decimal rounded to four decrnal places as needed )

Explanation / Answer

Solution:

Find the probability that the contribution margin for the product line exceeds the fixed cost of $3620.
The mean for the contribution margin for the product line is,
Mean = (12x 400)-(4 x400)
= 4800 -1600 = 3200
The variance for the contribution margin for the product line is,
Variance = (12^2x 900)+(3^2 x 1600) - ( 2 x 12 x 3x 20 x30 x 0.5)
= 129600 +14400 -21,600 = 12,2400
The standard deviation is,
Standard deviation = Variance = 12,2400 = 349.857
The required probability is,
P(X > 3,620) = 1-P(X 3620)
= 1- P(X-3200/349.857 3620-3200/349.857)
= 1- P(z 1.20)
= 1-0.1150 (From standard normal table)
= 0.885
Therefore, the probability that the contribution margin for the product line exceeds the fixed cost of $3620 is 0.885.

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