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Answer :
Answer:
Approximately 68.26% of tires wear out between 23,000 km and 27,000 km, 28.57% wear out between 26,000 km and 29,000 km, and 4% wear out by 21,498 km.
Step-by-step explanation:
Given: Normal distribution with Mean (μ) = 25,000 km and Standard Deviation (σ) = 2,000 km.
a. Percentage between 23,000 km and 27,000 km (μ ± 1σ):
Z-scores: -1.00 and +1.00
Percentage: 68.26%
b. Percentage between 26,000 km and 29,000 km:
Z-scores: 0.50 and 2.00
Percentage: P(0.50 ≤ Z ≤ 2.00) = P(Z ≤ 2.00) - P(Z ≤ 0.50) ≈ 0.9772 - 0.6915 = 0.2857
Percentage: 28.57%
c. Tire life (X) for which 4% have worn out (P(Tire Life ≤ X) = 0.04):
Z-score for 0.04 cumulative probability ≈ -1.751
X = μ + Zσ = 25,000 + (-1.751 * 2,000) ≈ 21,498 km
Tire Life: Approximately 21,498 km
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