# Central limit theorem

• May 15th 2011, 03:37 AM
Nforce
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?
• May 15th 2011, 03:45 AM
islam
hello
i think the expected value of x representing the number of 6's we get is supposed to be :
$\displaystyle 0.4*10000=4000$
• May 15th 2011, 03:48 AM
SpringFan25
islam has the answer, but its showing a latex error. ill just retype it with {tex} tags to remove the latex error:
Quote:

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

• May 15th 2011, 05:03 AM
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?)
• May 15th 2011, 06:57 AM
SpringFan25
yes, dont forget the continuity correction.
• May 15th 2011, 08:17 AM
CaptainBlack
Quote:

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 $\displaystyle 4000$, and the SD $\displaystyle =\sqrt{10000\times 0.4 \times 0.6} \approx 50$

CB