Question

Exhibit 5-9 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-9. What is the random variable in this experiment? Group of answer choices
a. the random sample of 5 voters
b. the number of registered voters in the nation
c. the number of female voters out of 5

Answer 1

Answer:

Let X the random variable of interest "number of registered voters" in a random sample of n =5, on this case we now that:  

$X \sim Binom(n=5, p=0.4)$  

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:  

$nCx=\frac{n!}{(n-x)! x!}$  

So then the best answer for this cas would be:

b. the number of registered voters in the nation

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

Let X the random variable of interest "number of registered voters" in a random sample of n =5, on this case we now that:  

$X \sim Binom(n=5, p=0.4)$  

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:  

$nCx=\frac{n!}{(n-x)! x!}$  

So then the best answer for this cas would be:

b. the number of registered voters in the nation