1. ## Central limit theorem

I need some help with this.

The probability to get 6 at each throw of a dice is 0.4(dice is unfair). We throw the dice 10 000 times and let X be the number of "6" in these throws.

What is the expected value for X?

Y is a random variable for each throw

Y ~
0 | 1
0.6| 0.4

I think it's correct, but what to do next?

2. ## hello

i think the expected value of x representing the number of 6's we get is supposed to be :
$0.4*10000=4000$

3. islam has the answer, but its showing a latex error. ill just retype it with {tex} tags to remove the latex error:
Originally Posted by islam
i think the expected value of x representing the number of 6's we get is supposed to be :
$0.4*10000=4000$

4. that seems reasonable. I thought i need a function.

What is the probability for X to be on the interval between 390 and 450?

Can I solve this with normal distribution? N ~(4000,sigma?)

5. yes, dont forget the continuity correction.

6. Originally Posted by Nforce
that seems reasonable. I thought i need a function.

What is the probability for X to be on the interval between 390 and 450?

Can I solve this with normal distribution? N ~(4000,sigma?)
Check this, since the mean is $4000$, and the SD $=\sqrt{10000\times 0.4 \times 0.6} \approx 50$

CB