A.  In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.

a. Which distribution should you use for this problem? Explain your choice.

b. Define the random variable X ¯ in words.

c. Construct a 95% confidence interval for the population mean cost of a used car.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a "95% confidence interval" means for this study.

Use the following information to answer the next two exercises: A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with a sample standard deviation of 1.55. Assume the underlying population is normally distributed.

B. An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709 randomly selected adults, 315 identified themselves as Latinos, 323 identified themselves as blacks, 254 identified themselves as Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said that they would welcome a white person into their families. Among Asians, 77% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person.

a. We are interested in finding the 95% confidence interval for the percent of all black adults who would welcome a

white person into their families. Define the random variables X and P′, in words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 95% confidence interval.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.