Let's address Lucilla's question by understanding her findings and deducing the possible ranges for the average weight of grapefruit from her six bags.
1. Calculation of the Minimum Weight:
- We inspect the given average weights: 7.1, 6.9, 7.3, 7.6, 8.1, 7.5.
- Among these values, the smallest weight is [tex]\(6.9\)[/tex] ounces.
2. Calculation of the Maximum Weight:
- Similarly, the largest weight among the given values is [tex]\(8.1\)[/tex] ounces.
3. Determining Possible Ranges for the Average Weight:
- We are given several potential ranges that represent the average weight:
1. 7.3 oz to 7.6 oz
2. 7.1 oz to 7.5 oz
3. 6.9 oz to 8.1 oz
4. 7.1 oz to 7.6 oz
To determine the correctness of these ranges, let’s validate them:
- For range 1 (7.3 oz to 7.6 oz):
- It covers the values: 7.3 and 7.6 which are within the min and max weights, so it’s feasible.
- For range 2 (7.1 oz to 7.5 oz):
- It includes the weights: 7.1 and 7.5 which also lie within the min and max weights.
- For range 3 (6.9 oz to 8.1 oz):
- This range includes all given weights since it starts from the min value (6.9) and goes up to the max value (8.1).
- For range 4 (7.1 oz to 7.6 oz):
- It encompasses values: 7.1 and 7.6, falling within the given range of weights.
Summary:
Given the provided sets of values and determined ranges:
- The possible accurate ranges for the average weight of a grapefruit include:
- [7.3, 7.6]
- [7.1, 7.5]
- [6.9, 8.1]
- [7.1, 7.6]
All these ranges are valid, and thus a grapefruit from a five-pound bag could weigh between any of these given ranges:
- 7.3 oz and 7.6 oz
- 7.1 oz and 7.5 oz
- 6.9 oz and 8.1 oz
- 7.1 oz and 7.6 oz
