Question 1

Think about what you know about DNA:

Credit: iStock/janiebros

1. How would you describe DNA to a friend, and what is it useful for?
2. What percentage of DNA do we share with our siblings? What about grandparents or cousins?

Question 2

The average amount of DNA a person shares with a sibling is normally distributed  with a mean of 50% and a standard deviation of 4%.^[1] On the following graph, label each tick mark on the x-axis below with the mean, mean [latex]\pm 1[/latex] standard deviation,  mean [latex]\pm 2[/latex] standard deviations, and mean [latex]\pm 3[/latex] standard deviations.

Question 3

Suppose you want to investigate the amount of DNA you share with your sibling.  You are interested in determining how likely it is that no more than 56% of your DNA  matches your sibling.

1. Identify where 56% should be on the curve you labeled in Question 2, and  then shade the area of the curve that represents the probability. Write a  mathematical expression to describe the shaded area.
2. Using your answer from Part a, estimate the probability (as a percentage) that your DNA matches no more than 56% of the DNA of your sibling. Choose the answer that is closest to the correct percentage.
   1. 5%
   2. 25%
   3. 50%
   4. 60%
   5. 90%
3. Estimate the probability (as a percentage) that your DNA matches more than  56% of the DNA of your sibling. Choose the answer that is closest to the  correct percentage.
   1. 5%
   2. 25%
   3. 50%
   4. 60%
   5. 90%

Question 4

The amount of DNA you share with a grandparent is normally distributed with an  average of 25% and a standard deviation of 3%.

1. Label the following graph with the mean, mean [latex]\pm 1[/latex] standard deviation, mean  [latex]\pm 2[/latex] standard deviations, and mean [latex]\pm 3[/latex] standard deviations.
   
2. Suppose you want to estimate the percentage of people who share less than  21% of their DNA with a grandparent. Label the curve at 21 and then shade  the area of the curve that represents the probability. Write a mathematical  expression describing the shaded area.
3. Use technology to calculate the percentage of people who share less than  21% of their DNA with a grandparent. Follow these steps:
   1. Go to the DCMP Normal Distribution tool at https://dcmathpathways.shinyapps.io/NormalDist/.
   2. Click on the Find Probability tab at the top.
   3. Type in the mean and standard deviation given in the question.
   4. Choose lower tail: [latex]P(X < x)[/latex].
   5. Type in the value of [latex]x[/latex]. In this case, it will be 21.
4. About what percentage of people would you expect share more than 21% of their DNA with a grandparent?

Question 5

The average amount of DNA you share with a first cousin is 12.5% with a standard deviation of 3.5%. What percentage of people do you expect share more than 19.5% of their DNA with their cousin? (Make sure to label and shade the following curve.

Question 6

Draw the curve from Question 5 again, and then draw a line where you think the top 1% would begin.

1. Hint: The top 1% of the area of the curve should be shaded. Round to the nearest hundredth.
   
2. We will now use technology to calculate the top 1%, which is also called the 99th percentile. The process is similar to how we found the probabilities in Questions 4 and 5, but instead of using the Find Probability tab, we will use the Find Percentile/Quantile tab since we are looking for a percentile. Round to the nearest hundredth.
   1. Go to the DCMP Normal Distribution tool at https://dcmathpathways.shinyapps.io/NormalDist/.
   2. Click on the Find Percentile/Quantile tab at the top.
   3. Type in the mean and standard deviation given in the question.
   4. Choose lower tail if we are looking for the bottom percent.
      Choose upper tail if we are looking for the top percent.
   5. Type in the probability in the lower tail/upper tail in % form.
3. Some people share very little DNA with their first cousins. What percentage of DNA is shared by the lowest 1%? Round to the nearest hundredth.

Question 7

If someone shared 21% of their DNA with a relative, would you expect that relative to be a sibling, grandparent, or first cousin? Explain.