If a normal model describes the page yield of printer ink cartridges, which statement must be true?

If a normal model describes the page yield of printer ink cartridges, which statement must be true?

• A. Most printers will yield exactly the average number of pages
• B. Some printers will yield significantly more or less than average
• C. All printers yield the same number of pages
• D. None

Answer: (B)

The assertion that some printers will yield significantly more or less than average is grounded in the properties of a normal distribution. In a normal model, data is symmetrically distributed around the mean, meaning that while many values cluster around the average, there is still a range of values on either side of this average. This inherent variability indicates that a subset of printers will naturally produce yields that deviate from the mean. Specifically, in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and about 95% lies within two standard deviations. This leads to the conclusion that it is not only possible but expected for there to be printers whose yields are significantly greater or lesser than the average. The other statements do not reflect this characteristic of normal distributions. For instance, asserting that most printers will yield exactly the average number of pages misrepresents the variability present in the data. Additionally, claiming all printers yield the same number of pages contradicts the very nature of the distribution, which allows for different yields. Therefore, the correct understanding aligns with the idea that variability in yield exists and that some printers are likely to yield notably different results from the average.

The assertion that some printers will yield significantly more or less than average is grounded in the properties of a normal distribution. In a normal model, data is symmetrically distributed around the mean, meaning that while many values cluster around the average, there is still a range of values on either side of this average.

This inherent variability indicates that a subset of printers will naturally produce yields that deviate from the mean. Specifically, in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and about 95% lies within two standard deviations. This leads to the conclusion that it is not only possible but expected for there to be printers whose yields are significantly greater or lesser than the average.

The other statements do not reflect this characteristic of normal distributions. For instance, asserting that most printers will yield exactly the average number of pages misrepresents the variability present in the data. Additionally, claiming all printers yield the same number of pages contradicts the very nature of the distribution, which allows for different yields. Therefore, the correct understanding aligns with the idea that variability in yield exists and that some printers are likely to yield notably different results from the average.