Current learring objective: Notation for the Binomiat: \( \mathrm{B}= \) Binomial Probability Distribution Function Question 12 Prev Score: O of 4 points The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only \( 18.6 \% \) of his customers buy a magazine and he thinks that he might be abie to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that \( 18.6 \% \) of his customers buy a magazine is correct, what is the probability that exactly 4 out of the first 14 customers buy a magazine? A 0.0699 B 0.2435 C 0.0240 D 0.1530

To find the probability that exactly 4 out of the first 14 customers buy a magazine, we can use the Binomial Probability Formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Where \( n = 14 \) (total customers), \( k = 4 \) (customers who buy a magazine), and \( p = 0.186 \) (probability of buying a magazine). Plugging these values in, we can calculate the probability. After calculating, you’ll find that the closest match to your options is **C 0.0240**. Probability calculations like this one are not only fun but also super useful in real-world scenarios, from business decisions like the deli’s to analyzing sales trends! Understanding binomial distributions can enhance strategic decision-making. It helps businesses forecast outcomes based on probability, making choices backed by statistical data rather than just intuition. Next time you’re faced with a choice, consider what the numbers might say about your potential success!