Entrepreneurship. A Gallup survey indicated that 75% of 18 to 29-year olds, given a choice, would prefer to start their own business rather than work for someone else. A random sample of 500 18 to 29-year olds is obtained.

a. Describe the sampling distribution (mean and standard deviation) of p^ , the sample proportion of 18 to 29-year olds who would prefer to start their own business.

b. In a random sample of 500 18 to 29-year olds, what is the probability that no more than 80% would prefer to start their own business?

c. Would it be unusual if a random sample of 500 18 to 29-year olds resulted in 250 or less who would prefer to start their own business (remember that unusual is more than 2 standard deviations from the mean)? Why or why not?