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?
Sales of $750 are outside three standard deviations of the mean.
In a normal distribution, values that deviate significantly from the mean can indicate unusual occurrences. With a mean of $1,500 and a standard deviation of $250, sales of $750 fall well beyond three standard deviations from the mean, signaling a potentially concerning drop in performance.
Sales of $750 represent a decrease of $750 from the mean, which is equivalent to a distance of three standard deviations below the mean (1,500 - 3 * 250 = 750). This significant deviation suggests that such low sales are highly unusual and may warrant concern for the salon's overall performance and customer demand.
This statement is incorrect because sales of $750 are not within two standard deviations of the mean. The range of two standard deviations from the mean would be from $1,000 to $2,000 (1,500 ± 2 * 250), and $750 falls outside this range, indicating an even more severe drop in sales.
While this option might seem plausible, it is incorrect as it misinterprets the statistical concept. Sales of $750 are actually at the extreme low end, being exactly three standard deviations below the mean, thus reinforcing the need for concern rather than suggesting that they are within a normal range.
This option is misleading as it incorrectly states that $750 represents a distance of two standard deviations from the mean. In reality, it is three standard deviations below the mean, making this statement factually incorrect and failing to recognize the severity of the sales drop.
In summary, the salon owner should be alarmed by sales of $750, as this figure is three standard deviations below the mean daily sales of $1,500. Such a significant deviation indicates an abnormality in sales patterns, which may require immediate attention to identify potential issues affecting the salon's revenue. Understanding standard deviations is crucial in assessing performance and making informed business decisions.
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