The magazine mass marketing company has received 16 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.5. What is the probability that no more than 12 of the entry forms will include an order?

1. Identify the parameters of the binomial distribution:
n = 16, \, p = 0.5, \, \text{and we need } P(X \leq 12)

2. Write the cumulative probability formula for the binomial distribution:
P(X \leq 12) = \sum_{k=0}^{12} \binom{16}{k} (0.5)^k (0.5)^{16-k}

3. Simplify the general term:
(0.5)^k \cdot (0.5)^{16-k} = (0.5)^{16}

4. Calculate the cumulative sum:
P(X \leq 12) = \sum_{k=0}^{12} \binom{16}{k} (0.5)^{16}

Using technology or tables:
P(X \leq 12) \approx 0.9717

Answer: The probability that no more than 12 of the entry forms will include an order is approximately 0.9717.