Final answer:
The acceptable weight of a bag of chips can be determined by evaluating the given inequality. By substituting different weights into the inequality, we can determine which statements are true. The correct statements are (A), (B), and (D).
Step-by-step explanation:
To determine which statements are true based on the given inequality |x – 250| < 0.8, we need to evaluate each statement.
(A) A bag of chips that weighs 251 grams is acceptable:
We substitute x = 251 into the inequality: |251 - 250| < 0.8
Simplifying, we get |1| < 0.8, which is true. Therefore, statement (A) is true.
(B) The difference between the maximum and minimum acceptable weights is 1.6 grams:
The maximum acceptable weight is found by adding 0.8 to the mean weight, while the minimum acceptable weight is found by subtracting 0.8 from the mean weight. So, the difference between the maximum and minimum acceptable weights is 0.8 + 0.8 = 1.6 grams. Therefore, statement (B) is true.
(C) The minimum acceptable weight of a bag of chips is 249.8 grams:
Since the mean weight is 250 grams, the minimum acceptable weight is 250 - 0.8 = 249.2 grams, not 249.8 grams. Therefore, statement (C) is false.
(D) A bag of chips that weighs 249.55 grams is acceptable:
We substitute x = 249.55 into the inequality: |249.55 - 250| < 0.8
Simplifying, we get |-0.45| < 0.8, which is true. Therefore, statement (D) is true.
Based on the analysis, the correct statements are (A), (B), and (D).