Question

Suppose a Normal Model describes the number of pages printer ink cartridges last. If we keep track of printed pages for the 47 printers at a company's office, which must be true?

1. The page counts for those ink cartridges will be normally distributed.
2. The histogram for those page count will be symmetric.
3. 95% of those page counts will be within 2 standard deviations of the mean.

Answer 1

If the distribution of ink cartridge page counts is normal and bell-shaped, roughly 95% of the data should lie within two standard deviations of the mean, and the histogram would be symmetric about the mean.

Step-by-step explanation:

When describing the page counts for ink cartridges in a normal distribution, there are a few key points to consider. Firstly, a normal distribution is defined by its symmetric, bell-shaped curve centered around the mean (µ), where the mean, median, and mode all lie at the same point on the graph. Additionally, the Empirical Rule tells us that for bell-shaped and symmetric data, approximately 95% of data will fall within two standard deviations from the mean.

Addressing the student's hypotheses: 1) Assuming the normal model is accurate, the page counts for those ink cartridges could be normally distributed, but this cannot be assured just by the model alone. 2) If indeed the page counts are normally distributed, the histogram should be symmetric about the mean. 3) According to the Empirical Rule, if the distribution is normal, then indeed 95% of the page counts are expected to lie within two standard deviations of the mean.