Posted by **Chelsea** on Tuesday, December 14, 2010 at 3:28am.

Given the population:

0,0,0,0,1,1,1,1,1,1

If a sample size of 6 was taken at random with replacement, what is the probability that the sample mean is 4/6?

- Statistics -
**TutorCat**, Tuesday, December 14, 2010 at 4:10pm
In order to get a mean of 4/6, you would need to pick four 1's and two 0's. The probability of picking a 1 (with replacement) is 6/10 each time and probability of picking a 0 (with replacement) is 4/10. So,

(6/10)*(6/10)*(6/10)*(6/10)*(4/10)*(4/10)

However, you can pick the four 1's and two 0's in any order. So, you perform

binomial expansion

N!/[K!(N-K)!]= number of possible ways that K individuals can be selected from N

10!/[4!(10-4)!]

Finally, take the product.

10!/[4!(10-4)!]*(6/10)*(6/10)*(6/10)*(6/10)*(4/10)*(4/10)=?

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