Just need 1.5

1. (30 points) According to the Original Tooth Fairy Poll (a real thing cited in a story on NPR's Planet Money podcast), the average gift received by a child who loses a tooth has increased with overall ination over the last couple of years and is now above $5 per tooth. However, the tooth fairy seems not to treat all teeth equally. Suppose that 80 percent of children receive $4 for each lost tooth, and the rest of the children receive $10 for each tooth. You plan to take a random sample of three children who have recently received a gift from the tooth fairy and compute the average gift they received, X. This question asks you to analyze the distribution of each respondent in your random sample, X ,-, as well as the distribution of the sample mean, X. 1.1. What is 130:, = 4)? 1.2. What is P(x,- = 10)? 1.3. What is mi = 4)? 1.4. What is 1%? z 6)? 1.5. What is mi = 8)? 1.6. What is 1361' = 10)? 1.7. What is E(X,-)? 1.8. What is 5(2)? 1.9. What is sd(X,')? 1.10. What is sd)