Final answer:
The probability calculations for the various scenarios involving customers ordering nonalcoholic beverages at Noodles & Company involve using the given probability of 0.52 for one customer and applying it to a sample of 11 customers.
Step-by-step explanation:
The question involves calculating the probability of various outcomes for customers ordering nonalcoholic beverages at a Noodles & Company restaurant, given a probability of 0.52 that any one customer will order a nonalcoholic beverage. Here's how to calculate each part:
- a. The probability that none of the 11 customers will order a nonalcoholic beverage is found by calculating (1 - 0.52)^11.
- b. The probability that at least 8 out of 11 customers will order a nonalcoholic beverage can be calculated using the binomial probability formula, summing the probabilities for exactly 8, 9, 10, and 11 customers ordering.
- c. The probability that fewer than 9 customers will order a nonalcoholic beverage is calculated by finding 1 minus the probability of 9 or more customers ordering.
- d. The probability that all 11 customers will order a nonalcoholic beverage is 0.52^11.