The Foggy Futures Weather Network offers an annual almanac for sale each year with information about predicted weather patterns, severe storm safety tips and a tracking chart. The finished product sells for $35, with a variable cost per unit of $21. The company has operating costs of $1,050,000. What is the probability of the firm having operating losses if the firm expects to sell 80,000 almanacs, with a standard deviation of 4,000 units? (A normal distribution table, for example, Table V from the text, must accompany this problem.)
A) 10.56%
B) 11.12%
C) 14.92%
D) 13.57%

Question

Quizplus · Accepted Answer

The probability of the firm having operating losses is 10.56%. This is because the expected profit is $1,050,000 - (80,000 * $21) = $210,000, and the standard deviation of profit is 4,000 * $14 = $56,000. Therefore, the z-score of the expected profit is 210,000 / 56,000 = 3.75. The probability of a z-score of 3.75 or less is 10.56%.

The Foggy Futures Weather Network Offers an Annual Almanac for Sale