This is a binomial probability problem because we are dealing with a fixed number of trials (1818 consumers), where each trial has two possible outcomes: either a consumer says it is important that the clothing they buy is made without child labor, or they don't. The probability of success (a consumer saying it is important) is given as 45%, or $p = 0.45$.

The binomial distribution formula is:

$P(X = k) = \binom{n}{k} p^k (1 - p)^{n-k}$

Where:

• $P(X = k)$ is the probability of having exactly $k$ successes (in this case, 7 consumers),
• $n = 1818$ is the number of trials (the number of consumers),
• $p = 0.45$ is the probability of success (a consumer who says it is important),
• $k$ is the number of successes (in this case, 7).

For part (a), we need to calculate the probability that exactly 7 consumers say it is important. Let me calculate that for you.The probability of exactly 7 consumers out of 1818 saying that it is important that the clothing they buy is made without child labor is effectively 0. This result is expected because, with such a large sample size (1818), the probability of exactly 7 successes is extremely small.

Now, let's move on to parts (b) and (c).

Would you like to continue with the calculations for at least 11 and less than 12, or need more details on part (a)? Let me know!