Answer :
To find the standard deviation of brown-eyed people at a convention, we use the binomial distribution formula with 6000 attendees and 68.7% probability, leading to an approximate value of 35.6.Therefore, the correct answer to this question is B
To find the standard deviation of the number of brown-eyed people at a gathering of 6000 people, where 68.7% of the population have brown eyes, you would 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, having brown eyes).
Given that \(n = 6000\) and \(p = 0.687\), the calculation would be:
\(\sigma = \sqrt{6000 \cdot 0.687 \cdot (1 - 0.687)}\)\
Plugging in the values, you get:
\(\sigma \approx \sqrt{6000 \cdot 0.687 \cdot 0.313}\)\
\(\sigma \approx \sqrt{1266.6}\)\
\(\sigma \approx 35.6\)\
Since the answer options are likely rounded, the closest answer is b. 35.9.
