Thank you for visiting 68 7 of the population have brown eyes A convention has 6000 people in attendance Find the standard deviation for the number of brown eyed. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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.
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