Answer: 0.023

## Explanation For a binomial distribution: - **Mean (E(X)) = np = 2** - **Variance (Var(X)) = np(1-p) = 1.5** ### Step 1: Find p and n From the variance formula: ``` Var(X) = np(1-p) = 1.5 2(1-p) = 1.5 (since np = 2) 1-p = 1.5/2 = 0.75 p = 1 - 0.75 = 0.25 ``` Now find n: ``` np = 2 n × 0.25 = 2 n = 2/0.25 = 8 ``` ### Step 2: Calculate P(X=5) Using the binomial probability formula: ``` P(X = 5) = C(8,5) × (0.25)^5 × (0.75)^3 ``` Where: - C(8,5) = 56 (combinations) - (0.25)^5 = 0.0009765625 - (0.75)^3 = 0.421875 Calculation: ``` P(X = 5) = 56 × 0.0009765625 × 0.421875 = 56 × 0.0004119873046875 = 0.0230712890625 ≈ 0.023 ``` Therefore, **P(X=5) = 0.023**, which corresponds to option B.

Author: Tanishq Prabhu