28. According to the US Census Bureau's American Community Survey, 87 percent of Americans over the age
of 25 have earned a high school diploma. Suppose we are going to take a random sample of 200 Americans
in this age group and calculate what proportion of the sample has a high school diploma. What is the
probability that the proportion of people in the sample with a high school diploma is less than 85 percent?
a) Write down the probability statement to calculate the probability of interest. Make sure to use the
correct notation. (3 marks)
b) Calculate the z-score needed to calculate the probability of interest. Write the formula used to calculate
the z-score, substitute the necessary values. Write the final answer to two decimal places. (4 marks)