Chapter 5 - Discrete Probability Distributions - 5-2 Mean, Variance, Standard Deviation, and Expectation - Exercises 5-2 - Page 273: 10

Mean = μ = ∑X * P(X) = (35*0.1)+(36*0.2)+(37*0.3)+(38*0.3)+(39*0.1) = 37.1 Variance = $ σ ^{2}$ = ∑[$X ^{2}$ * P(X)] - $ μ ^{2}$ =[ $35 ^{2}$ *0.1 +$36 ^{2}$ * 0.2 + $2 ^{2}$ 37 * 0.3 + $3 ^{2}$ 38 *0.3 + $39 ^{2}$ *0.1 ] -$37.1 ^{2}$ =1.29 Standard Deviation = σ = $ \sqrt σ ^{2}$ = $\sqrt 1.29$ = 1.1358 Standard Deviation = σ = $ \sqrt σ ^{2}$ = $\sqrt 1.29$ = 1.1358 The claim is not believable, because μ+3σ = 37.1+3(1.1358) = 40.5074, therefore 45 pizzas are not within 99% of confidence interval.