1. The problem involves understanding proportions in a population to plan a survey for launching new dishes. 2. We know 75% of customers are female and 25% are male. 3. To maximize the chance of a successful launch, the survey should reflect these proportions to get representative insights. 4. The formula for proportionate sampling is: $$\text{Sample size for group} = \text{Total sample size} \times \text{Proportion of group}$$ 5. For example, if the manager wants to survey 100 customers, then: - Female customers surveyed = $$100 \times 0.75 = 75$$ - Male customers surveyed = $$100 \times 0.25 = 25$$ 6. This ensures the survey results represent the customer base accurately, helping to make informed decisions for the new dishes. 7. Important rule: The sum of proportions must equal 1 (or 100%). Here, 0.75 + 0.25 = 1. 8. By conducting the survey quickly and proportionally, the manager can gather relevant insights efficiently.