Question: In an opinion poll, respondents were asked how they would vote...

Hi. I'm stuck on a question and would deeply appreciate any help with the following:

In an opinion poll, respondents were asked how they would vote for the possible opening of a new train station. Respondents were given two options when asked, either voting ‘yes’ or ‘no’. The respondents were a random sample of 400 from the entire population.

Assume 50% of the population voted ‘yes’.


Q1) What is the expected value of X? (X = yes votes)


Q2) What is the standard deviation of X?


Q3) In this poll, 180 people voted ‘yes’. Use the Central Limit theorem to approximate the probability that you would find 180 or fewer ‘yes’ votes from a random sample of 400.


Q4) Based on the results from Q3, explain how you would evaluate the claim that at least 50% of the population voted ‘yes’.

mazdamotor said:

In an opinion poll, respondents were asked how they would vote for the possible opening of a new train station. Respondents were given two options when asked, either voting ‘yes’ or ‘no’. The respondents were a random sample of 400 from the entire population.

Assume 50% of the population voted ‘yes’.

Q1) What is the expected value of X? (X = yes votes)

Click to expand...

Are the answers "yes" and "no" given numerical values?

mazdamotor said:

Q2) What is the standard deviation of X?

Click to expand...

Any given answer can only be "yes" or "no", rather than some combination thereof. The population as a whole voted half one way and half the other. This is similar to the situation in (this) discussion of the "mean" and "standard deviation" of tossing a fair coin.

(The rest of the article discusses these concepts within the context of opinion polls. Read the whole thing!)