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28 October, 20:22

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 percent of flight times are between 80 and 108 minutes?

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  1. 28 October, 23:38
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    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%
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