Questions: Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 78 times and recording the number of times the ball lands on green.

Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met.

Spinning an American roulette wheel 78 times and recording the number of times the ball lands on green.

Transcript text: Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 78 times and recording the number of times the ball lands on green.

Solution

Solution Steps

Step 1: Fixed Number of Trials

The procedure involves spinning an American roulette wheel \( n = 78 \) times. This satisfies the condition of having a fixed number of trials.

Step 2: Binary Outcomes

Each spin of the roulette wheel results in one of two outcomes: the ball either lands on green (success) or does not land on green (failure). This meets the requirement for binary outcomes.

Step 3: Independent Trials

The outcome of each spin is independent of the others. This means that the result of one spin does not affect the results of subsequent spins, fulfilling the independence condition.

Step 4: Constant Probability of Success

The probability of landing on green in a single spin of the American roulette wheel is given by: \[ p = \frac{2}{38} \] This probability remains constant across all trials, satisfying the condition for a constant probability of success.

Conclusion

Since all four conditions for a binomial distribution are met, we conclude that the procedure results in a binomial distribution.