Binomial Variable Scenarios Analysis
Which of the following may be modeled by a binomial random variable? If the binomial random variable is not appropriate, give a reason why.
- John is a 70% free-throw shooter. He decides to shoot 25 shots. We are interested in the number of successful shots. Assume the outcome on each shot is independent of all other shots.
- Margie is not very good at throwing darts. She is successful at hitting the bull’s eye about 30% of the time. We are interested in the number of throws it takes for her to hit the bull’s eye 10 times.
To determine if each scenario can be modeled by a binomial random variable, we need to consider the criteria for a binomial distribution:
- There are a fixed number of trials.
- Each trial has two possible outcomes (success or failure).
- The probability of success is constant for each trial.
- The trials are independent of each other.
Scenario 1: John’s Free-Throw Shots
- Description: John is a 70% free-throw shooter. He decides to shoot 25 shots. We are interested in the number of successful shots.
- Analysis:
- Fixed number of trials: Yes, John shoots 25 shots…
To determine if each scenario can be modeled by a binomial random variable, we need to consider the criteria for a binomial distribution:
- There are a fixed number of trials.
- Each trial has two possible outcomes (success or failure).
- The probability of success is constant for each trial.
- The trials are independent of each other.
Scenario 1: John’s Free-Throw Shots
- Description: John is a 70% free-throw shooter. He decides to shoot 25 shots. We are interested in the number of successful shots.
- Analysis:
- Fixed number of trials: Yes, John shoots 25 shots…
To determine if each scenario can be modeled by a binomial random variable, we need to consider the criteria for a binomial distribution:
- There are a fixed number of trials.
- Each trial has two possible outcomes (success or failure).
- The probability of success is constant for each trial.
- The trials are independent of each other. Binomial Variable Scenarios Analysis
Scenario 1: John’s Free-Throw Shots
- Description: John is a 70% free-throw shooter. He decides to shoot 25 shots. We are interested in the number of successful shots.
- Analysis:
- Fixed number of trials: Yes, John shoots 25 shots…
