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 outside the range that is considered typical for the business, being more than three standard deviations below the mean of $1,500.
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 for two standard deviations below the mean would be $1,500 - (2 * $250) = $1,000, meaning $750 is significantly lower than this threshold.
B) Sales of $750 are within three standard deviations of the mean.
This statement is incorrect. Sales of $750 are outside three standard deviations from the mean, which would be calculated as $1,500 - (3 * $250) = $750. Therefore, $750 represents the very limit of three standard deviations below the mean, not within it.
C) Sales of $750 are outside three standard deviations of the mean.
This option is correct. The mean sales figure is $1,500, and three standard deviations below the mean would be $750. Since $750 is at this threshold, technically it is the lowest point of acceptable sales, indicating that anything lower would be a cause for concern.
D) Sales of $750 are two standard deviations of the mean.
This option is incorrect. Sales of $750 do not equate to two standard deviations below the mean. Two standard deviations below the mean would be $1,000, meaning $750 is actually three standard deviations below the mean, which is not covered by this option.
Conclusion
In summary, the correct answer indicates that sales of $750 are outside three standard deviations of the mean, highlighting a significant deviation from average sales that warrants concern. All other options misinterpret the statistical boundaries set by the mean and standard deviations, failing to accurately assess the severity of the sales figure in relation to the salon’s performance.