Answer:
15.85%
Step-by-step explanation:
Empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviation and 99.7% falls within three standard deviation.
Given mean (μ) = 41 months, standard deviation (σ) = 5 months
One standard deviation = μ ± σ = 41 ± 5 = (36, 46)
Therefore 68% falls within 36 months and 41 months
Two standard deviation = μ ± 2σ = 41 ± 2(5) = (31,51)
Therefore 95% falls within 31 months and 51 months
Three standard deviation = μ ± 3σ = 41 ± 3(5) = (26, 56)
Therefore 99.7% falls within 26 months and 56 months
The percentage of cars that remain in service between 46 and 51 months = 32%/2 - 0.3%/2 = 16% - 0.15% = 15.85%
