American workers are increasingly planning to delay retirement (cnbc.com, Aug 25, 2019). A researcher finds that 35% of employed adults of age 62 and older say they have pushed back their retirement date.

a. What is the probability that in a sample of 100 employed adults of age 62 and older, more than 40% have pushed back their retirement date? 

b. What is the probability that in a sample of 200 employed adults of age 62 and older, more than 40% have pushed back their retirement date?

c. Comment on the difference between the two estimated probabilities.