Solve using R. Show all work. The Higher Education Research Institute at UCLA collected data from 302,458 incoming freshmenfrom 315 four-year college and universities in the United States. 67.1% of those students repliedthat, yes, they believe that same-sex couples should have the right to legal marital status. Supposethat you randomly pick eight freshmen from the survey. You are interested in the number thatbelieve that same-sex couples should have the right to legal marital status.XFind the probability that exactly 5 of the 8 freshmen sampled believe that same-sex couples shouldhave the right to legal marital status.Find the probability that at least 6 of the 8 freshmen sampled believe that same-sex couples shouldhave the right to legal marital status.Find the mean of the distribution.Find the standard deviation of the distribution.

Let X be the random variable that a number of freshmen believe that same-sex couples should have the…

X Find the probability that exactly 5 of the 8 freshmen sampled believe that same-sex couples should have the right to legal marital status. Find the probability that at least 6 of the 8 freshmen sampled believe that same-sex couples should have the right to legal marital status. Find the mean of the distribution. Find the standard deviation of the distribution.