5.(OS3: 3.34) Sickle cell anemia is a genetic blood disorder where red blood cells lose their flexibility and assume an abnormal, rigid, "sickle" shape, which results in a risk of various complications. If both parents are carriers of the disease, then a child has a 25% chance of having the disease, 50% chance of being a carrier, and 25% chance of neither having the disease nor being a carrier. If two parents who are carriers of the disease have 3 children, what is the probability that:

a. two will have the disease?

b. none will have the disease?

c. at least one will neither have the disease nor be a carrier?

d. the first child with the disease will the be 3rd child?

.75 x .75 x .25 = .140625

6.(OS3: 3.3 a-g) Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.

Write down the short-hand for these two normal distributions.

What is Sophia's Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section?Draw a standard normal distribution curve and mark these two Z-scores.

c. What do these Z-scores tell you?

d. Relative to others, which section did she do better on?

e. Find her percentile scores for the two exams

f. What percent of the test takers did better than her on the Verbal Reasoning section? On theQuantitative Reasoning section?

g. Explain why simply comparing raw scores from the two sections could lead to an incorrect conclusion as to which section a student did better on.

7.(OS3: 3.4 a-e) In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in theMen, Ages 30- 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups:

The finishing times of the Men, Ages 30 - 34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.

The finishing times of the Women, Ages 25 - 29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.2 - The distributions of finishing times for both groups are approximately Normal. Remember: a better performance corresponds to a faster finish.

a. Write down the short-hand for these two normal distributions.

b. What are the Z-scores for Leo's and Mary's finishing times? What do these Z-scores tell you?

c. Did Leo or Mary rank better in their respective groups? Explain your reasoning.

d. What percent of the triathletes did Leo finish faster than in his group?

e. What percent of the triathletes did Mary finish faster than in her group?

8.(OS3: 3.5) In Exercise 6 we saw two distributions for GRE scores: N(= 151,= 7) for the verbal part of the exam and N(= 153,= 7.67) for the quantitative part. Use this information to compute each of the following:

a. The score of a student who scored in the 80th percentile on the Quantitative Reasoning section.

b.The score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section.