65. 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?
Answer: A
Sales of $750 are outside three standard deviations of the mean.
Given that the mean daily sales are $1,500 with a standard deviation of $250, sales of $750 fall significantly below the expected range. Specifically, $750 is more than three standard deviations away from the mean, indicating a highly unusual and concerning sales figure.
A) Sales of $750 are outside three standard deviations of the mean.
This option is correct because three standard deviations below the mean would be calculated as $1,500 - (3 × $250) = $750. Since sales reached this exact figure, it indicates an extreme deviation from typical performance, which could signal a serious issue for the salon.
B) Sales of $750 are within two standard deviations of the mean.
This option is incorrect as two standard deviations from the mean would range from $1,000 to $2,000 ($1,500 ± $500). Sales of $750 are not within this range, indicating that this performance is below typical expectations.
C) Sales of $750 are within three standard deviations of the mean.
This option is incorrect because while $750 matches the calculation for three standard deviations below the mean, it does not fall within the range typically expected for normal operations. It indicates an extreme low, not a normal sales figure.
D) Sales of $750 are two standard deviations of the mean.
This option is incorrect as two standard deviations from the mean would yield a minimum of $1,000. Since $750 is below this threshold, it does not accurately describe the relationship between these numbers.
Conclusion
The correct answer, option A, highlights that sales of $750 are an extreme outlier, falling outside the expected range of normal sales activity. All other options inaccurately describe the statistical relationship, either misidentifying the standard deviation thresholds or incorrectly asserting that $750 is within normal ranges when it clearly is not. This significant drop in sales should raise immediate concern for the salon owner.