Question

7. The mean and standard derivation of binomial probability distribution are 36 and 3 respectively. Number of trials n is given by
[A] 42 [C] 48 [D] 24 [B] 36​

Answer 1

Concept:

Mean = μ = np

Where n = number of trials; p = probability of success; q = (1-p) = probability of failure

Calculation:

Given: Mean = μ = np = 12

∴ Variance = σ2 = npq = 4

⇒ 4 = np (1−p) = 12(1−p) 

 ⇒ 4/12 = (1−p) 

⇒ (1 – p) = 1/3

⇒ p = 1 – 1/3

∴ p = 2/3

Again; μ = np = 12

∴ n = 12/p = 12 × (3/2) = 18

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