# If we were to toss a single die (singular for dice) 1000 times, how many 6s could we expect over the long run? What is the standard deviation?

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Suppose you did this and got 200 6s. What is the z score of 200?

Suppose you did this and got 200 6s. What is the z score of 200?

##### 1 Answer

#### Explanation:

Let

- There is a fixed number of trials. (1000)
- The probability of the event occurring is constant. (1/6)
- Each throw of the die is independent.
- There are only two outcomes. (a 6 is thrown or it is not)

In general if we had a random variable

So we have

It can be shown that the expectation of the general binomial random variable

So,

and

As

The