Fifty-seven percent of families say that their children have an influence on their vacation plans. Consider a sample of eight families who are asked if their children influence their vacation plans. Identify the values of n, p, and q, and list the possible values of the random variable x.

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

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

And for this case we have:

n = 8 represent the sample random sample of families

p 0.57 represent the probability that say that their children have an influence on their vacation plans

q=1-p =1-0.57=0.43 represent the probability that say that their children NO have an influence on their vacation plans

And the possible values for the random variable are X=0,1,2,3,.....

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, on this case we now that:  

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

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

And for this case we have:

n = 8 represent the sample random sample of families

p 0.57 represent the probability that say that their children have an influence on their vacation plans

q=1-p =1-0.57=0.43 represent the probability that say that their children NO have an influence on their vacation plans

And the possible values for the random variable are X=0,1,2,3,.....

answer: 414,377,008

step-by-step explanation:

just multiply it