The Roger Company is introducing a new product. The product has fixed costs of \(\$ 200,000\) and variable costs of \(\$ 20\) per unit. Management is attempting to choose the more desirable of two possible prices. The prices, expected sales volume, and the standard deviation of the sales volume are as follows:

{Required:}
(1) For each possible price, calculate the probability of operating at a loss.
(2) For each possible price, calculate the probability of making at least \(\$ 60,000\) in profit.
(3) What price would you recommend for the new product? Why?

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Prices ....... $ 100 $ 120 2,500 220 Expected sales (units.)..................100 Standard deviation (units)............ 250 Assume that the use of the normal distribution is justified.