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Answer :
Final answer:
The least and most peppercorns a disposable grinder can contain based on the manufacturer’s criteria of z-scores between -0.9 and 0.9 are 317 and 327 peppercorns, respectively.
Explanation:
To calculate the least and most peppercorns a grinder can contain based on the z-score constraints, you need to use the mean and standard deviation along with the z-score formula:
Z = (X - μ) / σ
where Z is the z-score, X is the number of peppercorns, μ (mu) is the mean, and σ (sigma) is the standard deviation.
For a z-score of -0.9:
-0.9 = (X - 322) / 5.3
X = -0.9 * 5.3 + 322
X ≈ 317.23 peppercorns (rounded to the nearest whole number)
For a z-score of 0.9:
0.9 = (X - 322) / 5.3
X = 0.9 * 5.3 + 322
X ≈ 326.77 peppercorns (rounded to the nearest whole number)
Therefore, the grinder can contain between 317 and 327 peppercorns to meet the manufacturer's criteria.
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