Statistics S3 Central Limit Theorem Question

Hi.

I stumbled across a question which I don't know how to attempt to answer, but I do know that I would need to use the Central Limit Theorem, but I don't know how to do that with this question at all. Here it is:

A fair die is rolled 35 times.
a) Find the approximate probability that the mean of the 35 scores is more than 4.
b) Find the approximate probability that the total of the 35 scores is less than 100.

I'm stuck on part a) and I don't know how to find E(X) or Var(X) to set up the normal distribution parameters. Can anyone help?

Thanks!

(edited 11 years ago)

Reply 1

ghostwalker

Original post by Yoyo94

...

Start by working out the mean and variance of one roll of the die.

Then use what you know about sampling to find the mean and variance of the sample mean.

Reply 2

j4ckd4v13z

Well, for a single roll X, isn't

E(X) = 1.(1/6)+2.(1/6) +... +6.(1/6)

(And you work out Var(X) similarly)

(edited 11 years ago)

Reply 3

Yoyo94

Original post by ghostwalker

Start by working out the mean and variance of one roll of the die.

Then use what you know about sampling to find the mean and variance of the sample mean.

Original post by j4ckd4v13z

Well, for a single roll X, isn't

E(X) = 1.(1/6)+2.(1/6) +... +6.(1/6)

(And you work out Var(X) similarly)

Oh my goodness, I'm so retarded.. The number of throws is what got me confused. Thanks to the answerers above to whom I give credits and to whom I am very thankfulness towards, I just realised that my initial attempt to tackle the question was all wrong. I didn't realise that E(X) could have been calculated as j4ckd4v13z advised so I was completely stuck. Thank you for your help! It was really appreciated! :biggrin: