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22 October, 00:31

According to a surgery the top 10 employees in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minuets and the time spent is approximately a normal distribution. What are the times within which approximately 99.73 percent of all the workers will fall?

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  1. 22 October, 02:02
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    Answer: The times within which 99.73% workers fall are 252.2 and 573.2 minutes.

    Explanation:

    It is known that to capture approximately 99.73% of the mass (area) of the normal distribution one has to consider + / - standard deviations from the mean.

    The mean is 413 minutes and 1 standard deviation is 26.8 minutes. 6 standard deviations are 160.8 minutes.

    Therefore the minimum time is 413-160.8=252.2 minutes and the maximum time is 413+160.2=573.2 minutes.

    The times within which 99.73% workers fall are 252.2 and 573.2 minutes.
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