Consider four different Binomial distributions each with number of trials, n = 64 and probability of success, p as given in 1 to 4 below. Compute the variance for each Binomial distribution and arrange in ascending order. Choose the correct answer from the options given below:

With n fixed at 64, the binomial variance np(1-p) is smallest at p=0.01 and largest at p=0.5, giving the order 1, 4, 2, 3.

Distribution 1 with p=0.01 has variance 64 times 0.01 times 0.99, about 0.63, the smallest.

Distribution 4 with p=0.9 has variance 64 times 0.9 times 0.1, equal to 5.76.

Distribution 2 with p=0.3 has variance 64 times 0.3 times 0.7, equal to 13.44.

Distribution 3 with p=0.5 has variance 64 times 0.5 times 0.5, equal to 16, the largest.

Binomial variance is greatest at p=0.5 and shrinks symmetrically as p nears 0 or 1.