Match List I (n = number of Trials, p = Probability of Success) with List II (Mean and Standard Deviation of Binomial Distribution).

List I

i.N = 5, p = 0.4

ii.N = 6, p = 0.6

iii.N = 8, p = 0.5

iv.N = 7, p = 0.4

List II

a.2.8 and 1.296

b.2.0 and 1.095

c.4.0 and 1.414

d.3.6 and 1.200

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

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

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

Di-b, ii-d, iii-c, iv-a ✓ Correct

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

Explanation

Binomial mean equals n times p and standard deviation equals the square root of n p times one minus p, giving i-b, ii-d, iii-c, iv-a.

For n 5 and p 0.4 the mean is 2.0 and SD 1.095, matching option b.

For n 6 and p 0.6 the mean is 3.6 and SD 1.200, matching option d.

For n 8 and p 0.5 the mean is 4.0 and SD 1.414, matching option c.

For n 7 and p 0.4 the mean is 2.8 and SD 1.296, matching option a.

Variance of a binomial distribution is n p times one minus p.

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