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## Binomial Distribution Analysis Probability

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InstructionsBinomial Distribution Formulas:

Key:

n number of trials

k number of successes

p probability of success

1-p probability of not success, also sometimes denoted by q

(?(n@k)) n choose k , the number of ways to choose k things from a list of n things.

(?(n@k))=n!/(n-k)!k!Exactly k successes

Probability of getting exactly k successes out of n trials.P(x=k)=(?(n@k)) p^k (1-p)^(n-k)

In Excel this would be =BINOM.DIST(k,n,p,FALSE).At most k successes

Probability of getting at most k successes out of n trials.P(x?k)=?_(i=0)^k??(?(n@i)) p^i (1-p)^(n-i) ?

In Excel this would be =BINOM.DIST(k,n,p,TRUE).Less than k successes

Probability of getting less than k successes out of n trials.P(x<k)=?_(i=0)^(k-1)??(?(n@i)) p^i (1-p)^(n-i) ? In Excel this would be =BINOM.DIST(k-1,n,p,TRUE). At least k successes Probability of getting at least k successes out of n trials. P(x?k)=1-?_(i=0)^(k-1)??(?(n@i)) p^i (1-p)^(n-i) ? In Excel this would be =1-BINOM.DIST(k-1,n,p,TRUE). More than k successes Probability of getting more than k successes out of n trials. P(x>k)=1-?_(i=0)^k??(?(n@i)) p^i (1-p)^(n-i) ?

In Excel This would be =1-BINOM.DIST(k,n,p.TRUE).

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40-38 points

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83-76 points

Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.

52-49 points

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75-1 points

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