Final answer:
Upon calculating the standard deviation of the proportion for a survey with a 65% chance of having been to Europe, we find that the standard deviation is approximately 0.034. None of the given options perfectly match the calculated standard deviation of the number of people, suggesting the correct answer might be for the proportion instead.
Step-by-step explanation:
To estimate the standard deviation in a survey where there's a 65% chance that a participant had been to Europe, we can use the formula for the standard deviation of a binomial distribution, which is \(\sigma = \sqrt{n \cdot p \cdot (1 - p)}\), where n is the sample size and p is the probability of success. In this case, n = 200 and p = 0.65. So, the calculation for the standard deviation would be:
\(\sigma = \sqrt{200 \cdot 0.65 \cdot (1 - 0.65)}\)
\(\sigma = \sqrt{200 \cdot 0.65 \cdot 0.35}\)
\(\sigma = \sqrt{45.5}\)
\(\sigma\) is approximately 6.75, which suggest that none of the given options are correct. However, if we assume the student is looking for the standard deviation of the proportion rather than the number of people, the calculation would be different:
\(\sigma_p = \sqrt{\frac{p \cdot (1 - p)}{n}}\)
\(\sigma_p = \sqrt{\frac{0.65 \cdot 0.35}{200}}\)
\(\sigma_p = \sqrt{0.0011375}\)
\(\sigma_p\) is approximately 0.034, which is one of the provided options and likely the correct answer.