Final answer:
The probability that none of the 14 customers at Noodles & Company will order a nonalcoholic beverage, when the probability of any customer ordering one is 0.50, is approximately 0.0061%.
Step-by-step explanation:
The probability that a customer will order a nonalcoholic beverage at Noodles & Company restaurant is 0.50. To find the probability that in a sample of 14 customers, none will order a nonalcoholic beverage, you use the formula for the probability of 'none' in a binomial distribution setting where the number of trials is n and the probability of success (in this case ordering a nonalcoholic beverage) is p.
Thus, the desired probability is (1 - p)^n. Plugging in the values:
Probability = (1 - 0.50)^14 = 0.5^14 = 0.00006103515625.
So, the probability that none of the 14 customers will order a nonalcoholic beverage is approximately 0.000061 or 0.0061%.