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28 July, 13:25

A random sample of computer startup times has a sample mean of x¯=37.2 seconds, with a sample standard deviation of s=6.2 seconds. Since computer startup times are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two times are approximately 95% of the data? Round your answer to the nearest tenth

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  1. 28 July, 14:25
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    95% of the data lies between 24.8 and 49.6

    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

    - A random sample of computer startup times has a sample mean of

    μ = 37.2 seconds

    ∴ μ = 37.2

    - With a sample standard deviation of σ = 6.2 seconds

    ∴ σ = 6.2

    - We need to find between what two times are approximately 95%

    of the data

    ∵ 95% of the data lies within two standard deviations

    ∵ Two standard deviations (µ ± 2σ) are:

    ∵ (37.2 - 2 * 6.2) = 24.8

    ∵ (37.2 + 2 * 6.2) = 49.6

    ∴ 95% of the data lies between 24.8 and 49.6

    * 95% of the data lies between 24.8 and 49.6
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