Question

The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% 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.

What is the probability that at least two of the freshmen reply "yes"? (Round your answer to four decimal places.)

Answer 1

Given:- 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital.

8 freshmans are choosen

Answer:- p =0.713 and n=8

We use binomial distribution because number of trial is finite and probability of succcess (p) is constant .

Let X is number of freshman randomly choosen.

Therefore, q =1 - p = 0.287

P( X >= 2) = 1 - P(X=0) - P(X =1)

= 1 - 0.000046 - 0.00091

= 0.9990

Therefore probability that at least two are freshmen is 0.9990