The daily sales from a salon are normally distributed with a mean of $1,500 and a standard deviation of $250. The salon owner notices that sales were $750 on a particular day.
Why should the owner be concerned about sales based on this scenario?
A.
Sales of $750 are within three standard deviations of the mean.
B.
Sales of $750 are two standard deviations of the mean.
C.
Sales of $750 are outside three standard deviations of the mean.
D.
Sales of $750 are within two standard deviations of the mean.
In a normal distribution, most observations fall withinthree standard deviations of the mean. This principle is central to data-driven decision making and statistical process control. Values outside this range are considered highly unusual and may indicate an underlying problem.
Here, the mean is $1,500 and the standard deviation is $250. Three standard deviations below the mean equals $750 ($1,500 − 3 × $250). Sales of exactly $750 fall at the extreme lower boundary, indicating an unusually low sales day.
Such an outcome signals a potential anomaly that warrants investigation, such as operational issues, staffing shortages, or external disruptions. Values this far from the mean occur very infrequently in normal conditions.
Therefore, the owner should be concerned because sales of $750 areoutside the typical operating range, making optionCthe correct answer.
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