In Exercise 5.29, we see that the distribution of sample proportions of US adults with a college degree for random samples of size n = 500 is N(0.275, 0.02). How often will such samples have a proportion, p̂, that is more than 0.30?

Exercise 5.29

According to the US Census Bureau,4 about 27.5% of US adults over the age of 25 have a bachelor’s level (or higher) college degree. For random samples of n = 500 US adults over the age of 25, the sample proportions, p̂, with at least a bachelor’s degree follow a normal distribution with mean 0.275 and standard deviation 0.02. Draw a sketch of this normal distribution and label at least three points on the horizontal axis.