A random variable X counts the number of successes in 20 ind

A random variable X counts the number of successes in 20 independent trials. There is the same probability of success for each trial. If the probability of exactly 1 success in the 20 trials is (20 1) (0.4)^1(0.6)^19, what is sigma x? (a) 8 (b) 12 (c) 4.8 (d) 2.2 (e) 3.2 (f) None of the above.

Solution

As we can see from the formula he used, it is a binomial distributed variable.

Thus,

sigma(x) = sqrt(npq)

As

n = 20
p = 0.4
q = 0.6

Then

sigma(x) = sqrt(20*0.4*0.6) = 2.19089023 = 2.2 [ANSWER, D]