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Express Courier Service has found that the delivery time for packages is normally distributed with mean 14 hours and standard deviation 2 hours. What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time? (Hint: note that 5% of the packages will be delivered at a time beyond the guarantee time period)

  • math -

    It would seem that you are only concerned with packages that would take longer than normal time to delivered. "Beyond" could infer either direction.

    95% = mean + 1.645 SD

    Insert value and solve.

    If it were either direction:

    95% = mean ± 1.96 SD

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