Question

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 82 times and recording the number the ball lands on.

answer
yes
no
there are more than two possible outcomes on each trial of the experiment.
the experiment does not consist of \\(n\\) identical trials.
the trials are dependent.

Explanation:

Analyze the requirements of a binomial experiment

Using the Binomial Distribution knowledge point
A binomial experiment must satisfy four conditions:

1. The experiment consists of a fixed number of trials, \(n\).
2. The trials are independent.
3. Each trial has only two possible outcomes (success and failure).
4. The probability of success, \(p\), remains constant for each trial.

Evaluate the given procedure

Using the Binomial Distribution knowledge point
The procedure is: "Spinning an American roulette wheel 82 times and recording the number the ball lands on."

• There is a fixed number of trials (\(n = 82\)).
• The trials are independent.
• However, recording the actual number the ball lands on results in 38 possible outcomes (numbers 1-36, 0, and 00) on each trial, rather than exactly two outcomes.
• Therefore, this procedure does not result in a binomial distribution because there are more than two possible outcomes on each trial.

Answer:

• Yes
• No
• There are more than two possible outcomes on each trial of the experiment. (Correct answer)
• The experiment does not consist of n identical trials.
• The trials are dependent.