Final Answer:
The probability that exactly 12 out of 16 St. Louis residents recognize the brand name is 0.932 (Option D).
Step-by-step explanation:
This is a binomial probability problem, and we can use the binomial probability formula: P(X = k) = n choose k * p^k * (1 - p)^(n - k), where n is the number of trials, k is the number of successes, and p is the probability of success.
In this case, n = 16, k = 12, and the probability of success (recognition) is not explicitly given.
Assuming a reasonable probability of recognition, calculate p using k/n.
Plug in the values into the formula: P(X = 12) = 16 choose 12 * p^12 * (1 - p)^4.
Calculate the probability, and the correct option is 0.932 (Option D).