Are these bionomial? If not, explain why. A.)Approx 5% of a school district's 1000 seniors have...

Are these bionomial? If not, explain why.

A.)Approx 5% of a school district's 1000 seniors have no siblings. A random sample of 300 seniors is taken from that district, and X counts the number with no siblings.

B.) Approx 5% of high school seniors have no siblings. A random sample of 200 high school seniors is taken and X counts the number with no siblings.

C.) Approx 5% of high school seniors have no siblings, 29% have one, 27% have two and the remaining 39% have three or more. A random sample of 100 high school seniors is taken and the random variable X counts the number of siblings for each of the sampled seniors.

Solutions

Expert Solution

A) This is not binomial because the given 5% is a sample estimate based on one single school's data. And X is counting the number of senior with no siblings in the random sample of 300 seniors FROM ENTIRE DISTRICT. In order for X to be binomial distributed random variable, the proportion of success must be a population proportion. Since, here it is a sample estimate, the success proportion on each senior is not constant.

B) Yes, this is Binomial. Because given success proportion is On the entire Population of high school seniors. And each senior can be assumed to be independent of all other for having a sibling. And success proportion is constant on each senior of the 200 sample size. Hence, X is counting the number of successes on a fixed number of trials, each trial is independent of others. Success proportion is same on each trial.

C) No, this is not a Binomial. Because X counts the number of siblings for each senior. For X to be binomial, we want it to model no.of successes in a fixed number of trials.

orchestra answered 1 year ago

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