Question

According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal, June 26, 2008). Suppose eight individuals are randomly selected. What is the probability that none will delay or go without medical care?

Answer 1

`P(X=0)=(8C0)(0.2)^0 (1-0.2)^(8-0)=0.1677`

Explanation:

1) 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".

2) Solution to the problem

Let X the random variable of interest "Number of americans that delay or go without medical care because of concerns about cost", on this case we now that:

`X \sim Binom(n=8, p=0.2)`

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=(n!)/((n-x)! x!)`

And we want to find this probability:

`P(X=0)`

So we can replace into the probability mass function and we got:

`P(X=0)=(8C0)(0.2)^0 (1-0.2)^(8-0)=0.1677`