Binomial & Normal Distributions

Worked: ready-mix acceptance

A batch plant’s records show 5% of truckloads are rejected at the site. Of the next 10 loads, P(exactly one rejected) = 10 × 0.05 × 0.95⁹ = 0.5 × 0.630 = 0.315. P(none rejected) = 0.95¹⁰ = 0.599, so P(at least one) = 1 − 0.599 = 0.401.

The same plant’s 28-day strengths are normal with μ = 4,500 psi and σ = 400 psi. The share below 4,000 psi: z = (4,000 − 4,500)/400 = −1.25, and the table gives 0.106 — about one cylinder in nine.