Question

People with a body mass index (BMI) of over 30 are considered obese. Recent reports indicate the rate of obesity is climbing nation-wide. In the 2011 report, Mississippi had the highest obesity rate, at 34.5% of adults. Georgia was in eighteenth place at 30.4%, while Colorado ranked last in obesity at 19.8%. If we selected a random sample of 1,000 adults from these three states and observed the number of obese individuals in the sample, X _______ (will or will not) have a binomial distribution.

Answer 1

The observed number of obese individuals in the selected sample of 1000 from the three states will not have a binomial distribution, because the three states have different probability of being obese.

Explanation:

The probability of success of a binomial distribution is p and the probability of failure is q or (1 -p). Therefore, since the three states have different probabilities, the number of obese individuals from a random selection of 1000 individuals from the three states will not have a binomial distribution.

Binomial distribution in probability represents a distribution with possible outcomes of either a success or failure, that is, it represents the likelihood of having a given amount successes, x from a number of trials, n, where the probability of success per trial is given as p.

The binomial distribution means a distribution that has two likely outcomes which is either a success or failure.

Example of a binomial distribution includes, tossing of coin, pass or fail, or defined success or failure, such as the likelihood of rolling a three and the likelihood of rolling any other value.