During the presidential elections in Froggyland, two candidates challenge each other: **Marine** and **Emmanuel**.

**N.B.** Any resemblance with real people would be purely fortuitous.

These are the results of the last survey concerning the results of the election, published on Saturday before the election:

The survey used a sample of **1,000 people**. We will assume that this sample is representative, and that those surveyed didn't lie about their vote.

Emmanuel thinks he is guaranteed to win the election โthe winner being the candidate who gets the most votes.

**Is he right? Or is there a slight chance Marine could beat him?**

EinsteinJr
Aug 7, 2017

#1**0 **

I'll give a simple answer, cause i'm lazy.

520 ppl voted for Emmanuel and 480 ppl voted for Marine.

If that is the total population of Froggyville, then yes, Emmanuel has a very high probability of winning. But if not, then Marine still has a chance.

as i said, im lazy

Mathhemathh
Aug 8, 2017

#2**0 **

... Yup. Lazy ๐

**HINT:** I am waiting you to use a confidence interval, that gives you the upper and lower bounds the proportion of supporters of Emmanuel, depending on the frequency observed (in that case, 52 %), and with a confidence of about 95 %.

Here is the formula:

\(f-\frac{1}{\sqrt{n}}\leq p \leq f+\frac{1}{\sqrt{n}}\)

where *p* corresponds to the proportion of people who will actually vote for Emmanuel, *f* is the proportion of the people **surveyed** who said they would vote for him, and *n* is the size of our sample (the number of people surveyed).

EinsteinJr
Aug 8, 2017