Flight times for commuter planes are normally distributed, with a mean time of 94 minutes and a standard deviation of 7 minutes. Using the empirical rule, approximately what percentage of flight times are between 80 and 108 minutes.

32%

68%

95%

99.7%

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%