Match List-I (n = number of trials, p = probability of success) with List-II (variance of the binomial distribution) and choose the correct answer from the options given below.

List I

i.N = 7, p = 0.3

ii.N = 5, p = 0.4

iii.N = 8, p = 0.5

iv.N = 6, p = 0.6

List II

a.1.44

b.2.00

c.1.20

d.1.47

Ai-a, ii-b, iii-c, iv-d

Bi-b, ii-c, iii-d, iv-a

Ci-c, ii-d, iii-a, iv-b

Di-d, ii-c, iii-b, iv-a ✓ Correct

Correct answer: (D) i-d, ii-c, iii-b, iv-a

Explanation

The binomial variance equals n times p times one minus p, giving i-d, ii-c, iii-b, iv-a.

With n 7 and p 0.3 the variance is 1.47.

With n 5 and p 0.4 the variance is 1.20.

With n 8 and p 0.5 the variance is 2.00.

With n 6 and p 0.6 the variance is 1.44.

Binomial variance is largest when p equals one half.

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