36. 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: C
Sales of $750 are outside three standard deviations of the mean.
Sales of $750 are significantly lower than the average daily sales of $1,500, falling outside three standard deviations from the mean, which indicates an unusual and concerning drop in sales for the salon.
A) Sales of $750 are two standard deviations of the mean.
This option is incorrect because sales of $750 actually fall more than two standard deviations below the mean. The calculation shows that two standard deviations below the mean would be $1,500 - (2 x $250) = $1,000. Therefore, $750 is not merely two standard deviations away.
B) Sales of $750 are within two standard deviations of the mean.
This option is incorrect as well. Since $750 is below $1,000 (which is two standard deviations below the mean), it is not within two standard deviations. This suggests that the sales figure is significantly lower than what would be expected under normal circumstances.
C) Sales of $750 are outside three standard deviations of the mean.
This option is correct. The calculation for three standard deviations below the mean results in $1,500 - (3 x $250) = $750. Since $750 equals this value, it indicates that it is on the boundary of three standard deviations, suggesting a significant anomaly in sales performance.
D) Sales of $750 are within three standard deviations of the mean.
This option is incorrect. For a normal distribution, being within three standard deviations would imply that sales should be above $750, as it falls precisely on the threshold. Thus, it does not accurately represent the normal range of sales.
Conclusion
The correct answer is that sales of $750 are outside three standard deviations of the mean, indicating a major concern for the salon owner due to an unusual drop in sales. All other options misinterpret the statistical implications of the data, failing to recognize the severity of a sales figure that is at the extreme end of the distribution.