Answer:
μ ≈ 2.33
σ ≈ 1.25
Explanation:
Each person has equal probability of ⅓.
![\left[\begin{array}{cc}X&P(X)\\1&(1)/(3)\\2&(1)/(3)\\4&(1)/(3)\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/gpymxwqqcl03fit7x71cvihzx5ij7yngza.png)
The mean is the expected value:
μ = E(X) = ∑ X P(X)
μ = (1) (⅓) + (2) (⅓) + (4) (⅓)
μ = ⁷/₃
The standard deviation is:
σ² = ∑ (X−μ)² P(X)
σ² = (1 − ⁷/₃)² (⅓) + (2 − ⁷/₃)² (⅓) + (4 − ⁷/₃)² (⅓)
σ² = ¹⁴/₉
σ ≈ 1.25