Question

According to an NBC news report, 1 in 20 children in the U.S. have some type of food allergy. We select a random sample of 25 children and let X = the number in the sample who have a food allergy. Question 1: Which type of probability distribution best describes the problem?

Answer 1

Answer:

For this case the best distribution would be the binomial since we have a value of n given and fixed representing the random sample and on each experiment we have a Bernoulli trial with a probability of success always 1/20 and failure 19/20.

Let X the random variable of interest, on this case the distribution would be given by:

$X \sim Binom(n=25, p=1/20)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

For this case the best distribution would be the binomial since we have a value of n given and fixed representing the random sample and on each experiment we have a Bernoulli trial with a probability of success always 1/20 and failure 19/20.

Let X the random variable of interest, on this case the distribution would be given by:

$X \sim Binom(n=25, p=1/20)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$