Problem 38

Given information

• The Higher Education Research Institute at UCLA collected data from incoming first-time, full-time freshmen from four-year colleges and universities in the U.S.
• % of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status.
• Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.
• Number of trials, = 8, and probability of success, = % or .

Concept:- 

                Binomial distribution:- When the event of interest is ‘number of successes’ in conducting a random experiment with trials,                                                                                                 that is when and where, binomial distribution is used.

                A random variable is said to follow a binomial distribution if it satisfies the following conditions:-   

                1) There are only two possible outcomes of each trial i.e., success and failure.

                2) The number of trials is finite.

                3) The probability of success is constant for each trial.

                4) The trials are independent of each other.

To find:  ~ _____(_____,_____)

Step-by-step explanation

As per the given question,

                   Definition of random variable can be put up as being the number of freshmen who believe that marriage of same-sex couples should be duly                                   acknowledged as completely legal.