Answer:
The percent of flight times is 95%
Step-by-step explanation:
* Lets revise the empirical rule
- The Empirical Rule states that almost all data lies within 3
standard deviations of the mean for a normal distribution.
- The empirical rule shows that
# 68% falls within the first standard deviation (µ ± σ)
# 95% within the first two standard deviations (µ ± 2σ)
# 99.7% within the first three standard deviations (µ ± 3σ).
* Lets solve the problem
- Flight times for commuter planes are normally distributed, with a
mean time of 94 minutes
∴ μ = 94
- The standard deviation is 7 minutes
∴ σ = 7
- One standard deviation (µ ± σ):
∵ (94 - 7) = 84
∵ (94 + 7) = 101
- Two standard deviations (µ ± 2σ):
∵ (94 - 2×7) = (94 - 14) = 80
∵ (94 + 2×7) = (94 + 14) = 108
- Three standard deviations (µ ± 3σ):
∵ (94 - 3×7) = (94 - 21) = 73
∵ (94 + 3×7) = (94 + 21) = 115
∵ The percent of flight times are between 80 and 108 minutes
∴ The empirical rule shows that 95% of the distribution lies
within two standard deviation in this case, from 80 to 108 minutes
* The percent of flight times is 95%
