*Please use this template for your answers*.

# Wedding Planner

You got a new job as “Wedding Planner”. Your clients want to organize a big party, but they are not sure how many people will attend. Talking to your clients, you find that they have:

- 10 good friends that will probably attend to the party,
- 50 regular friends that may or may not attend, and
- 40 acquittances (i.e. people they know but that are not
*really*friends) that must be invited but that will probably not attend

Each one of the good friends will attend with probability 90%. The regular friends will attend with probability 50%. The acquittances will attend with probability 20%.

## 1. Simulate one party

The function `party`

receives the number of good, regular and bad friends, and returns the total number of people attending to the simulated party.

```
<- function(n_good, n_regular, n_bad) {
party # write your code here
}
```

If all is right, you should get something like this:

`party(10, 50, 40)`

`[1] 48`

## 2. Simulate ten thousand parties

Store the result in a vector called `parties`

, and make a bar plot

`# write your code here`

`barplot(table(parties))`

## 3. Mean value and standard deviation

Find the average and the standard deviation of the number of people attending the party

`# write your code here`

```
[1] 42.0306
[1] 4.415225
```

## 4. Find an interval containing 95% of all parties

This will allow you to have a reasonable idea of what will happen in real life.

You should get something like this

`[1] 33.20015 50.86105`

`# write your code here`

## 5. Find population mean using a small sample

In a previous question we found the mean value of `parties`

, assuming that we know all of them.

Now we will assume that the vector `parties`

is a population, and we have only access to a small sample of 3 cases.

`<- sample(parties, size=3) sample_of_3 `

Please find an interval containing the population mean with 95% confidence

`[1] 33.74417 48.92250`

Attention:this question is different from the previous one. Here we ask for an interval forthe population mean, not for the individual cases.

## 6. Find population mean using a larger sample

Repeat the same procedure as before, assuming that you have a sample of 20 cases.

`<- sample(parties, size=20) sample_of_20 `

Please find an interval containing the population mean with 95% confidence

`[1] 39.13881 43.52786`