Final answer:
The probability of fewer than 30% of consumers in a sample of 100 choosing sustainable brands can be calculated using normal distribution approximation. This involves finding the Z-score for k = 29 and corresponding to the cumulative probability, given that 57% is the probability of any one consumer choosing 'good' brands.
Step-by-step explanation:
The student is asking about the probability that in a sample of 100 consumers, fewer than 30% are choosing to buy from brands they believe are doing social or environmental good. Given that an international study reveals 57% of consumers are making such choices, we can apply the binomial or normal distribution approximation to solve this problem.
To find this probability, we use the following steps:
- Identify the success probability (p) as 0.57 since 57% of consumers buy from 'good' brands.
- Find the number of consumers in the sample (n), which is 100.
- The question asks for the probability that fewer than 30 consumers (which is 30% of 100) choose 'good' brands. This corresponds to k < 30, where k is the number of successes.
- Since n is large, we can use the normal approximation to the binomial distribution. Here the mean (μ) is np, and the standard deviation (σ) is √(npq), where q = 1 - p.
- Use these parameters to find the Z-score for k = 29, then use the standard normal distribution table or a calculator to find the corresponding cumulative probability.
This probability reflects consumer behavior regarding sustainability, a key factor for corporations aiming to be profitable over the long term while managing their environmental, economic, and social impacts. With rising consumer pressure and environmental advocacy, companies are increasingly aligning with sustainable and eco-friendly practices to meet consumer demand and contribute to a more sustainable global society.