1.) A scale measuring ageism (age discrimination) has been administrated to a large sample of human resources managers at major corporations. The distribution of scores is approximately normal with mean 31 and a standard deviation of 5. What proportion of the large sample had scores between 26 and 33? Show all of your steps. Writing down the final answer without work will not receive any marks.

2.)According to the Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States is normally distributed and has a mean of 13.6 and a standard deviation of 3.0. These values are unknown to a researcher who samples self-employed individuals to estimate mean number of years of education. Suppose she takes a random sample of 23 self-employed individuals.

a.) What is the sampling distribution? Explain why we can construct the distribution.

b.) Find the 95% confidence interval for the mean number of years of education for self- employed individuals.

c.) Suppose that they found a sample with a mean number given by y = 15. Is this unusual? Explain.