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Answer :
To determine the standard deviation for the number of brown-eyed people at a convention with 6000 attendees, calculate the expected number of brown-eyed individuals, and then use the binomial distribution formula. The final standard deviation is approximately 35.9. Therefore, the correct option is B.
The problem presented requires us to find the standard deviation for the number of brown-eyed people at a convention with 6000 people, given that 68.7% of the population have brown eyes. First, we calculate the expected number of brown-eyed individuals by multiplying the percentage by the total number of people at the convention: 0.687 imes 6000 = 4122. This is the mean ( extbf{mean}) of our distribution.
Next, to find the standard deviation ( extbf{standard deviation}), we use the formula for the standard deviation of a binomial distribution, which is extbf{ extbf{ extit{sd}}} = extbf{ extbf{ extit{sqrt}}}(np(1-p)), where 'n' is the total number of trials (people) and 'p' is the probability of success (having brown eyes). Thus, extbf{ extbf{ extit{sd}}} = sqrt(6000 imes 0.687 imes (1 - 0.687)) = extbf{ extbf{ extit{sqrt}}}(6000 imes 0.687 imes 0.313) extapprox 35.9. Therefore, the standard deviation is approximately 35.9, which means the answer is option b. 35.9. Therefore, the correct option is B.
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