Can someone help me with a Statistic problem?

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SUMMARY

The discussion focuses on calculating the expected value and 95% confidence bounds for a binomial distribution in a survey scenario where 30% of respondents are expected to choose Route A. The participants are tasked with plotting these values as a function of sample size n, ranging from 50 to 800. Key statistical concepts such as the binomial distribution and expectation value are central to solving this problem.

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  • Basic concepts of expectation value in statistics
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Statisticians, data analysts, and students studying probability and statistics who are looking to deepen their understanding of binomial distributions and confidence intervals.

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Consider a survey of n people asking whether they plan to use Route A or Route B, with an anticipated fraction p choosing Route A.

If p = .30, plot the 95% confidence bounds and the expected value of X as a function of n, for n = 50 to n = 800.

I have no idea where to start or how to work it out..can someone please guide me through the problem.
 
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There are two possible outcomes - a person chooses A or B, so a binomial distribution applies.

What have you learned about the expectation value?
 

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