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?
Sales of $750 are outside three standard deviations of the mean.
In a normal distribution, a value that falls outside three standard deviations from the mean is considered highly unusual. Given the mean of $1,500 and a standard deviation of $250, sales of $750 are significantly lower and warrant concern for the salon owner.
This statement is incorrect because two standard deviations from the mean would range from $1,000 ($1,500 - 2*$250) to $2,000 ($1,500 + 2*$250). Since $750 falls below this range, it cannot be classified as within two standard deviations.
This choice is incorrect as well because three standard deviations from the mean encompass a range from $750 ($1,500 - 3*$250) to $2,250 ($1,500 + 3*$250). While $750 is at the lower limit, the statement implies it is within the range, which may mislead the owner into thinking sales are acceptable.
This is the correct answer, as $750 is exactly three standard deviations below the mean of $1,500. In statistical terms, any value beyond this threshold is considered an outlier, indicating that the day's sales are significantly lower than expected.
This option is incorrect because sales of $750 represent the lower boundary of three standard deviations from the mean, not two. Two standard deviations would suggest a higher minimum threshold of $1,000, making this claim inaccurate.
The salon owner should be concerned about the sales of $750 since this figure is precisely at the cutoff for three standard deviations below the mean of $1,500. Values outside this range are statistically unusual and may indicate underlying issues that need to be addressed to ensure the business's financial health. Recognizing such anomalies is crucial for effective management and decision-making.
Related Questions
View allWhat is an omission error?
In an experimental study, researchers are testing a new flea preventiv...
A hot tub company recently calibrated all its machines during an expen...
A political ballot gives voters the option to vote for one of three ca...
Which type of analysis determines whether there was a significant diff...
Related Quizzes
View all0PC1 Planning Instructional Strategies for Meaningful Learning Version 1
AP01 Elementary Literacy Curriculum Version 1
AQ01 Applied Healthcare Statistics C784 Version 1
ASO1 Introduction to Statistics for Research Version 1
BJ01 Introduction to Business Finance Version 1
C172 Network and Security Foundations Version 1
C180 Introduction to Psychology Version 1
C180 Introduction to Psychology Version 2
CKC1 Introduction to Humanities Version 1
DZ01 Mathematics for Elementary Educators III MATH 1330 Version 1
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations