62. 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.
The salon owner should be concerned because sales of $750 fall significantly below the average, indicating a potential issue with business performance. Specifically, this amount is more than three standard deviations from the mean, suggesting an unusual and concerning drop in sales.
A) Sales of $750 are within two standard deviations of the mean.
This option is incorrect because sales of $750 are actually more than two standard deviations below the mean. The range of two standard deviations from the mean of $1,500 (which is $1,000 to $2,000) does not include $750.
B) Sales of $750 are within three standard deviations of the mean.
This statement is also incorrect. Sales of $750 are not within three standard deviations of the mean; instead, they fall outside of this range. The three standard deviations from the mean extend from $750 to $2,250, making $750 the lower boundary.
C) Sales of $750 are outside three standard deviations of the mean.
This option is correct as it accurately describes the statistical situation. The mean is $1,500, and three standard deviations below this mean reaches $750. Since $750 is precisely at the lower limit, any sales below this level indicate that performance is significantly poorer than normal.
D) Sales of $750 are two standard deviations of the mean.
This option is incorrect. Sales of $750 do not represent two standard deviations from the mean. In fact, two standard deviations below the mean would be $1,000, indicating that $750 is not even within the acceptable range for two standard deviations.
Conclusion
The correct answer is option C, as sales of $750 clearly indicate performance that is statistically significant and concerning, falling outside the three standard deviations range. All other options misinterpret the standard deviation thresholds, leading to incorrect conclusions about the salon's sales performance.