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.
Sales of $750 are significantly lower than the average daily sales, falling outside three standard deviations of the mean, which indicates an extreme event that could warrant concern for the salon owner.
A) Sales of $750 are outside three standard deviations of the mean.
This option is correct because the mean is $1,500, and three standard deviations below the mean would be $1,500 - (3 × $250) = $750. Since sales reached exactly $750, this indicates that the sales are at the threshold of being considered an outlier, suggesting a drastic drop that is statistically significant.
B) Sales of $750 are within two standard deviations of the mean.
This option is incorrect. Two standard deviations below the mean would be $1,500 - (2 × $250) = $1,000. Since $750 is below this threshold, it is not within two standard deviations and indicates a more serious deviation from normal sales.
C) Sales of $750 are within three standard deviations of the mean.
This option is misleading. While $750 is the exact value that represents three standard deviations below the mean, it does not imply that it is within the standard range of normal sales; it is the cutoff point that suggests an extreme deviation.
D) Sales of $750 are two standard deviations of the mean.
This option is incorrect. Two standard deviations below the mean would be $1,000, making $750 below this range. Thus, it misrepresents the relationship of $750 to the calculated standard deviations.
Conclusion
The correct answer, A, accurately reflects the statistical significance of daily sales at $750 being at the extreme low end of the normal distribution. All other options misinterpret the relationship between the sales figure and the established mean and standard deviations, failing to recognize the potential issue for the salon owner regarding such low sales figures.