![]() What is the probability that exactly 8 of 10 report relief? We can use the same method that was used above to demonstrate that there is a 30.30% probability that exactly 8 of 10 patients will report relief from symptoms when the probability that any one reports relief is 80%. What is the most likely number of patients who will report relief out of 10? If 80% report relief and we consider 10 patients, we would expect that 8 report relief. Interpretation: There is practically no chance that none of the 10 will report relief from symptoms when the probability of reporting relief for any individual patient is 80%. What is the probability that none report relief? We can again use the binomial distribution model with n=10, x=0 and p=0.80. Where x= # of 'successes', n = # of replications or observations, and p = probability of success on a single observation. Place the cursor into an empty cell and enter the following formula: Note: Binomial probabilities like this can also be computed in an Excel spreadsheet using the =BINOMDIST function. Interpretation: There is a 20.13% probability that exactly 7 of 10 patients will report relief from symptoms when the probability that any one reports relief is 80%.
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