Let's solve the problem step-by-step.
1. Identify the given values and the true density of aluminum:
- Aluminum's true density = 2.7 g/ml
- Recorded densities from the classes:
- 1st hour: 3.1 g/ml
- 2nd hour: 3.05 g/ml
- 3rd hour: 1.9 g/ml
- 4th hour: 2.35 g/ml
- 5th hour: 4.2 g/ml
- 6th hour: 4.0 g/ml
2. Compare each class’s density value to the true density:
- Values under the true density (2.7 g/ml):
- 3rd hour: 1.9 g/ml
- 4th hour: 2.35 g/ml
- Values over the true density (2.7 g/ml):
- 1st hour: 3.1 g/ml
- 2nd hour: 3.05 g/ml
- 5th hour: 4.2 g/ml
- 6th hour: 4.0 g/ml
3. Group the values based on the criteria provided in the options:
- Option a:
- Group: 1st, 3rd, 5th, and 6th hours, with one recorded decimal place in their values.
- Group: 2nd and 4th hours, with two recorded decimal places in their values.
This option does not group exclusively based on the density values being under or over the true density.
- Option b:
- Group: 3rd and 4th hours, with values under the true density.
- Group: 1st, 2nd, 5th, and 6th hours, with values over the true density.
This option groups the data correctly based on whether the densities are under or over the true density.
- Option c:
- Group: 3rd hour, with a 1 value.
- Group: 4th hour, with a 2 value.
- Group: 1st and 2nd hours, with 3 values.
- Group: 5th and 6th hours, with 4 values.
This option groups the densities based on numerical values assigned to some unspecified criteria, which does not match the problem's requirement relating to true density.
- Option d:
- Group all classes as accurate.
This option is not applicable because not all class values are equal to the true density.
Based on the above-given criteria and comparison, the correct grouping based on accuracy relative to the true density is:
Answer: (b) Group: 3rd and 4th hours, with values under the true density. Group: 1st, 2nd, 5th, and 6th hours, with values over the true density.
