Question

a binomial model shows that two outcomes have the same probability of occurring. in an experiment with 60 trials to test this model, the researcher found that outcome a occurred 36 times. how did the experimental outcome compare to the theoretical model? outcome b occurred 36% of the time rather than the expected 50%. outcome a had an expected probability of 50% but an actual probability of 36%. the result for outcome b was 4 less than expected. the result for outcome a was 6 more than expected.

Explanation:

Step1: Calculate expected number of occurrences for each outcome

In a binomial model with two equally - likely outcomes and 60 trials, the expected number of occurrences for each outcome is $\frac{60}{2}=30$.

Step2: Analyze Outcome A

Outcome A occurred 36 times. The difference between the experimental and expected number of occurrences for Outcome A is $36 - 30=6$. So, the result for Outcome A was 6 more than expected.

Step3: Analyze Outcome B

Outcome A occurred 36 times, so Outcome B occurred $60 - 36 = 24$ times. The difference between the expected (30) and experimental (24) number of occurrences for Outcome B is $30-24 = 6$ (not 4). Also, the actual probability of Outcome A is $\frac{36}{60}\times100\%=60\%$ (not 36%), and the actual probability of Outcome B is $\frac{24}{60}\times100\% = 40\%$ (not 30%).

Answer:

The result for Outcome A was 6 more than expected.