Answer:
So, the middle 90% probability interval for the weight of a single hamburger is approximately \(167.1\) grams to \(232.9\) grams.
Explanation:
Certainly, let's calculate the values using the given information:
Given:
- Mean (\(\mu\)): 200 grams
- Standard Deviation (\(\sigma\)): 20 grams
- Z-score for .05 quantile: -1.645
- Z-score for .95 quantile: 1.645
Substitute these values into the formulas:
\[ \text{Lower bound} = 200 - 1.645 \times 20 \]
\[ \text{Upper bound} = 200 + 1.645 \times 20 \]
Calculating:
\[ \text{Lower bound} = 200 - (1.645 \times 20) = 200 - 32.9 = 167.1 \]
\[ \text{Upper bound} = 200 + (1.645 \times 20) = 200 + 32.9 = 232.9 \]
So, the middle 90% probability interval for the weight of a single hamburger is approximately \(167.1\) grams to \(232.9\) grams.