According to a 2004 report from the Centers for Disease Control, 5% of teenagers are gay or lesbian.
a. Find the mean and standard deviation of sample proportion who are gay or lesbian for random samples of 400 teenagers.
b. Tell why the distribution of sample proportion for random samples of 400 teenagers will have a shape that is approximately normal.
c. Use the 68-95-99.7 Rule to sketch the distribution of sample proportion for samples of size 400 taken from a population where the proportion who are gay or lesbian is 0.05.
d. If 160 in a sample of 400 homeless teenagers are found to be gay or lesbian, does this suggest that homeless teenagers are not representative of teenagers in general with respect to sexual orientation? Use the value of standardized sample proportion (z) to justify your answer.
e. If 160 in a sample of 400 homeless teenagers are found to be gay or lesbian, does this lend support to claims that many teenagers who tell their parents they are gay are thrown out of their homes? Explain.