According to the Graduate Management Admission Council, applications to two-year MBA programs have been on the decline during the past few years. A survey during 2016 reported that 43% of U.S. schools experienced fewer applications when compared to 2015. A random sample of eight U.S. schools with a two-year MBA program was selected.

a. What is the probability that exactly two schools from this sample experienced a decline in applications in 2016?

b. What is the probability that more than five schools from this sample experienced a decline in applications in 2016?

c. What is the probability that three or fewer schools from this sample experienced a decline in applications in 2016?

d. What are the mean and standard deviation for this distribution?