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Analyze a Larger Set of Data for a Dihybrid Cross

Below is data for 250 offspring mice, as produced in a laboratory.

\begin{tabular}{|r|c|c|c|c|}
\cline {2-5}
\multicolumn{1}{c|}{} & \begin{tabular}{c}
Black Fur and \\
Black Eyes
\end{tabular} & \begin{tabular}{c}
Black Fur and \\
Red Eyes
\end{tabular} & \begin{tabular}{c}
White Fur and \\
Black Eyes
\end{tabular} & \begin{tabular}{c}
White Fur and \\
Red Eyes
\end{tabular} \\
\hline
Predicted Fraction & [tex]$9 / 16$[/tex] & [tex]$3 / 16$[/tex] & [tex]$3 / 16$[/tex] & [tex]$1 / 16$[/tex] \\
\hline
Predicted Percentage & [tex]$56.25\%$[/tex] & [tex]$18.75\%$[/tex] & [tex]$18.75\%$[/tex] & [tex]$6.25\%$[/tex] \\
\hline
Laboratory Fraction & [tex]$155 / 250$[/tex] & [tex]$51 / 250$[/tex] & [tex]$44 / 250$[/tex] & [tex]$20 / 250$[/tex] \\
\hline
Laboratory Percentage[tex]$^*$[/tex] & [tex]$62\%$[/tex] & [tex]$20.4\%$[/tex] & [tex]$17.6\%$[/tex] & [tex]$8.0\%$[/tex] \\
\hline
\end{tabular}

Notice that the predicted percentages and laboratory percentages are not the same. These differences most likely result from [tex]$\square$[/tex]

Sagot :

GinnyAnswer
The differences between the predicted percentages and the laboratory percentages most likely result from natural variation due to random genetic assortment and the finite size of the sample population.

Here's a step-by-step analysis:

1. Understanding Predicted Percentages:
- The dihybrid cross uses the predicted genotypic ratios based on Mendelian genetics for a cross of two heterozygotes (AaBb x AaBb).
- The predicted fractions 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]
- These can be converted to predicted percentages by multiplying each fraction by 100:
- [tex]\( \frac{9}{16} \times 100 = 56.25\% \)[/tex]
- [tex]\( \frac{3}{16} \times 100 = 18.75\% \)[/tex]
- [tex]\( \frac{3}{16} \times 100 = 18.75\% \)[/tex]
- [tex]\( \frac{1}{16} \times 100 = 6.25\% \)[/tex]

2. Understanding Laboratory Percentages:
- The actual observed laboratory data for 250 offspring mice are converted to percentages to compare with predicted values:
- Black Fur and Black Eyes: [tex]\( \frac{155}{250} \times 100 = 62\% \)[/tex]
- Black Fur and Red Eyes: [tex]\( \frac{51}{250} \times 100 = 20.4\% \)[/tex]
- White Fur and Black Eyes: [tex]\( \frac{44}{250} \times 100 = 17.6\% \)[/tex]
- White Fur and Red Eyes: [tex]\( \frac{20}{250} \times 100 = 8.0\% \)[/tex]

3. Comparing Predicted and Laboratory Percentages:
- Predicted percentages vs. Laboratory percentages:
- Black Fur and Black Eyes: 56.25% predicted vs. 62% observed
- Black Fur and Red Eyes: 18.75% predicted vs. 20.4% observed
- White Fur and Black Eyes: 18.75% predicted vs. 17.6% observed
- White Fur and Red Eyes: 6.25% predicted vs. 8.0% observed

4. Reason for Differences:
- Random Genetic Assortment: Genetic assortment during reproduction is a random process, and even though there's an expected probability based on Mendelian genetics, the actual outcomes can vary in a finite sample.
- Finite Sample Size: When dealing with a finite sample of 250 offspring, it's common to see some deviations from the predicted fractions due to the small size of the sample relative to an infinite population.

Therefore, we conclude that the differences between the predicted percentages and the laboratory percentages are most likely due to natural variation arising from the random genetic assortment and the finite size of the sample population.
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