According to a Gallup poll conducted August 7–10, 2014, 48% of American workers said that they were completely satisfied with their jobs. Assume that this result is true for the current population of American workers.

a. Find the probability that in a random sample of 1150 American workers, the proportion who will say they are completely satisfied with their jobs is

i. greater than .50 

ii. between .46 and .51

iii. less than .45 iv. between .495 and .515

v. less than .49 vi. more than .47

b. What is the probability that in a random sample of 1150 American workers, the proportion who will say they are completely satisfied with their jobs is within .025 of the population proportion?

c. What is the probability that in a random sample of 1150 American workers, the proportion who will say they are completely satisfied with their jobs is not within .03 of the population proportion?

d. What is the probability that in a random sample of 1150 American workers, the proportion who will say they are completely satisfied with their jobs is greater than the population proportion by .02 or more?