Chapter 5 - Discrete Probability Distributions - 5-2 Mean, Variance, Standard Deviation, and Expectation - Exercises 5-2 - Page 272: 4

Mean = μ = ∑X * P(X) = (5*0.05)+(6*0.2)+(7*0.4)+(8*0.1)+(9*0.15)+(10*0.1) = 7.4 Variance = $ σ ^{2}$ = ∑[$X ^{2}$ * P(X)] - $ μ ^{2}$ =[ $5 ^{2}$ *0.05 +$ 6 ^{2}$ * 0.2 + $7 ^{2}$ * 0.4 + $ 8 ^{2}$ *0.1 + $ 9 ^{2}$ *0.15 + $10 ^{2}$ *0.1 ] -$ 7.4 ^{2}$ =56.6-54.76 =1.84 Standard Deviation = σ = $ \sqrt σ ^{2}$ = $\sqrt 1.84$ = 1.3565

--