Answer:
The percent of flight times between 80 and 108 minutes is 95% ⇒ 3rd answer
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.
- 68% of the data falls within one standard deviation.
- 95% of the data lies within two standard deviations.
- 99.7% of the data lies Within three standard deviations
- 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 and a standard deviation of 7 minutes
∴ μ = 94
∴ σ = 7
- One standard deviation (µ ± σ):
∵ (94 - 7) = 87
∵ (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
- We need to find the percent of flight times between 80 and 108 min
∵ The empirical rule shows that 95% of the distribution lies within
two standard deviation in this case, between 80 and 108 min
∴ The percent of flight times between 80 and 108 minutes is 95%
