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?

Question

Mathematics

Barbara Baker

7 September, 12:16

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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Mikayla Curry · Answer 1

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.