Bouncy Bungee Rubber Band Company has fixed costs of $2,760,000 per year, it sells its rubber bands for $3.75 per pack, and the variable cost of these packs is $0.75. They estimate they will sell 1,000,000 packs this year, with a standard deviation of 40,000 units. Find the probability of the company incurring a loss. (A normal distribution table, for example, Table V from the text, must accompany this problem.)
A) 3.22%
B) 6.71%
C) 5.48%
D) 2.87%

Question

Quizplus · Accepted Answer

To find the probability of the company incurring a loss, we first calculate the break-even point in units, then determine the z-score for the break-even point, and finally use the normal distribution to find the probability.1. Calculate the break-even point in units:$$ \text{Break-even point in units} = \frac{\text{Fixed Costs}}{\text{Price per unit} - \text{Variable Cost per unit}} $$$$ = \frac{2,760,000}{3.75 - 0.75} = \frac{2,760,000}{3} = 920,000 \text{ units} $$2. Calculate the z-score for the break-even point:$$ \text{Z} = \frac{\text{Break-even point} - \text{Mean}}{\text{Standard Deviation}} $$$$ = \frac{920,000 - 1,000,000}{40,000} = \frac{-80,000}{40,000} = -2 $$3. Use the normal distribution table to find the probability corresponding to a z-score of -2. This gives us a probability of 2.28% for being below the mean, but since we're looking for the probability of incurring a loss, which is the lower tail beyond the break-even point, we refer to the correct table or calculation method for the cumulative probability up to a z-score of -2, which typically is around 2.28%. However, the correct answer (C) 5.48% suggests there might have been a misunderstanding in the calculation or interpretation of the normal distribution values. The correct approach involves understanding how the distribution applies to the scenario, but without the specific table or calculation error provided, the explanation is based on standard procedure for these types of problems. The discrepancy in the final answer suggests a need for clarification or a specific interpretation of the normal distribution table used.

Bouncy Bungee Rubber Band Company Has Fixed Costs of $2,760,000