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?
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