Central limit theorem
Probability theory · Mathematics
Study notes
Q: Battery lifetimes average 500 hours, SD 50. For 100 batteries, find P(mean > 510). SE = 50/√100 = 5. By CLT, X̄ ≈ N(500, 5²). Z = (510-500)/5 = 2. P(Z > 2) = 1 - 0.9772 = 0.0228. Only 2.3% chance the average exceeds 510 hours!