1. According to the 2008 GSS the mean age of Americans when their rst child was born is 23.76 with a standard deviation of 5.364. This distribution is positively skewed (right tailed). a) Is the median age at rst birth higher or lower than 23.76? How do you know? (2 points) b) If you standardized these ages what would be the shape of the distribution? Why? (2 points) 2. Calculate the following probabilities (don't forget to draw your picture!): a) P(Z2.14) (1 point) e) P(Z>-2 .42 & z1.64) (2 points) 3. Assume that scores among Asian Americans on an alienation scale have the following distribution: N (22.3, 2.1), with higher scores reecting greater feelings of alienation. The distribution of scores on this alienation scale for Native Americans has a u of 21.7 and a G of 3.8. Use this information to answer the following questions (don't forget to draw your picture and answer in a complete sentence!): a) What proportion of Asian Americans score between 20 and 25? (6 points) b) What is the probability that a randomly selected Native American scores below 13.5? (4 points) c) What proportion of Asian Americans score above 22? (5 points) d) What would be the percentile ranking of a Native American who scored 20.1? (4 points) e) Kevin (an Asian American) and John (a Native American) both answered questions to the alienation scale. If Kevin scored 18.? and John scored 15.9 who is feeling more alienated relative to those in the same racial group? Explain (6 points) i) What score would an Asian American have to achieve to be in the 87th percentile on the alienation scale? (4 points) g) A community center in Arizona wants to develop programs to reduce alienation among Asian Americans and Native Americans. With limited funding they decide to target the top 2% (most alienated) in each group. What scores do individuals in each group have to have in order to qualify for these programs? (6 points)