### Step-by-Step Solution
Let's analyze the given problem systematically to understand the differences between the predicted and laboratory percentages of offspring mice.
#### 1. Laboratory Data:
We have data from a laboratory experiment with 250 offspring mice. The categories are:
- Black Fur and Black Eyes: [tex]\( \frac{155}{250} \)[/tex]
- Black Fur and Red Eyes: [tex]\( \frac{51}{250} \)[/tex]
- White Fur and Black Eyes: [tex]\( \frac{44}{250} \)[/tex]
- White Fur and Red Eyes: [tex]\( \frac{20}{250} \)[/tex]
#### 2. Predicted Data:
The predicted fractions for the same categories are:
- Black Fur and Black Eyes: [tex]\( \frac{9}{16} \)[/tex]
- Black Fur and Red Eyes: [tex]\( \frac{3}{16} \)[/tex]
- White Fur and Black Eyes: [tex]\( \frac{3}{16} \)[/tex]
- White Fur and Red Eyes: [tex]\( \frac{1}{16} \)[/tex]
Let's calculate the corresponding percentages for predicted fractions:
- Black Fur and Black Eyes: [tex]\( \frac{9}{16} \times 100 = 56.25\% \)[/tex]
- Black Fur and Red Eyes: [tex]\( \frac{3}{16} \times 100 = 18.75\% \)[/tex]
- White Fur and Black Eyes: [tex]\( \frac{3}{16} \times 100 = 18.75\% \)[/tex]
- White Fur and Red Eyes: [tex]\( \frac{1}{16} \times 100 = 6.25\% \)[/tex]
#### 3. Laboratory Percentages:
The laboratory percentages, based on their observed data, are:
- Black Fur and Black Eyes: [tex]\( 62\% \)[/tex]
- Black Fur and Red Eyes: [tex]\( 20.4\% \)[/tex]
- White Fur and Black Eyes: [tex]\( 17.6\% \)[/tex]
- White Fur and Red Eyes: [tex]\( 8.0\% \)[/tex]
#### 4. Differences Between Predicted and Laboratory Percentages:
To understand the discrepancy, let's find the absolute differences between the predicted and observed percentages:
- Black Fur and Black Eyes: [tex]\( |62 - 56.25| = 5.75\% \)[/tex]
- Black Fur and Red Eyes: [tex]\( |20.4 - 18.75| = 1.65\% \)[/tex]
- White Fur and Black Eyes: [tex]\( |17.6 - 18.75| = 1.15\% \)[/tex]
- White Fur and Red Eyes: [tex]\( |8.0 - 6.25| = 1.75\% \)[/tex]
These differences highlight the variances between what was predicted and what was observed in the laboratory.
#### 5. Conclusion:
The differences between the predicted percentages and the laboratory percentages likely result from natural experimental variation. In any biological experiment involving a sample population, we can expect some degree of variation due to factors like random sampling error, environmental influences, genetic variation, and other stochastic elements. This means that even if the predicted ratios are based on sound genetic principles, real-world results can differ slightly due to these intrinsic variations.
