Statistics

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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 -

    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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