Decide whether the experiment is a binomial, Poisson, or neither based on the information given. Each week a man plays a game in which he has a 21% chance of winning the random variable is the number of times he wins in 64 weeks.
A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.A survey of adults found that 62% have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the past 12 months.
To determine whether the given experiment can be considered as a binomial or Poisson experiment, we need to consider the properties of each and see which one aligns with the given information.
A binomial experiment requires the following conditions:
1. There must be a fixed number of trials.
2. Each trial must have only two possible outcomes, typically referred to as success and failure.
3. The probability of success must remain constant for each trial.
4. The trials must be independent of each other.
On the other hand, a Poisson experiment is characterized by the following conditions:
1. It measures the number of events that occur in a fixed unit of time, space, or other interval.
2. The events must occur independently of each other.
3. The average rate of occurrence (λ) should be constant.
Given that the random variable is the number of times the man wins in 64 weeks, we can determine the type of experiment based on the conditions mentioned above.
In this case, the experiment is not a binomial experiment because the probability of winning is not fixed and constant. It is mentioned that the man has a 21% chance of winning, which implies that the probability changes from week to week. Therefore, Condition 3 for a binomial experiment is not met.
On the other hand, this experiment aligns with the conditions of a Poisson experiment. The experiment measures the number of events (wins) that occur in a fixed unit of time (64 weeks). The wins are independent of each other, and although the average rate of occurrence is not explicitly given, we can assume it remains relatively constant throughout the 64 weeks. Hence, based on the information given, the experiment is more likely to be a Poisson experiment.