If you have a population of 3,000,000 people, how many to be sampled to give a representative profile with only a 5% point margin of error?

To determine the sample size needed to give a representative profile with a 5% point margin of error in a population of 3,000,000 people, we need to use a statistical formula.

First, let's understand a few key terms:
1. Population: The total number of individuals in the group we want to study (in this case, 3,000,000 people).
2. Sampling Size: The number of individuals we need to include in our sample.
3. Margin of Error: The maximum acceptable difference between the sample estimate and the true population parameter (in this case, 5% point margin of error).
4. Confidence Level: The degree of confidence in the results, typically expressed as a percentage.

To calculate the required sample size, we need to consider the margin of error, confidence level, and the size of the population. The formula to calculate the sample size is:

Sample Size = (Z^2 * p * (1-p)) / (E^2)

Where:
- Z is the Z-score corresponding to the desired confidence level. For a 95% confidence level, the Z-score is approximately 1.96.
- p is the estimated proportion of the population expected to have a particular characteristic. If there is no prior estimate, we usually assume 0.5 for maximum variability.
- E is the margin of error, expressed as a decimal. In this case, it is 0.05.

Given that we assume maximum variability (p = 0.5), the formula can be simplified to:

Sample Size = (1.96^2 * 0.5 * (1-0.5)) / (0.05^2)

Plugging in the values:

Sample Size = (3.8416 * 0.5 * 0.5) / 0.0025
Sample Size = 0.9604 / 0.0025
Sample Size = 384.16

Rounding up to the nearest whole number, the required sample size would be 385.

Therefore, to obtain a representative profile with a 5% point margin of error in a population of 3,000,000 people, you would need to sample 385 individuals.