please help me find the standard deviation of this question

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. 71.4% 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 six 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 standard deviation (𝜎)? (Round your answer to four decimal places.)

Answer 1

Let X be the number of first-time, full-time freshmen that believe that same-sex couples should have the right to legal marital status.

We can identify that X~Binom (n=6,p=0.714) based on the following reasoning:

(1) There are a fixed number of independent trials. (There are 6 trials because we are choosing 6 freshmen and they are independent because the outcome of one trial doesn't affect the outcomes of the other trials.)

(2) Each trial has the same probability of success, p=0.714.

Now, we know that the standard deviation of a binomial distribution SD(X)= √np(1-p). So to find the standard deviation, we can substitute n=6, p=0.714, (1-p)=0.286.

The answer is 1.106.

(note: SD(X)= √np(1-p) may also be written as SD(X)= √npq )