Please show all steps and work used to derive the answer. I’m more interested in making sure that I understand how to use formulas and correct processes properly, rather than just the right answer. 

According to creditcard.com, 29% of adults do not own a credit card.

a. Suppose a random sample of 500 adults is asked, “Do you own a credit card?” describe the sampling distribution of p?, the proportion of adults who own a credit card?

b. What is the probability that in a sample of 500 adults, more than 30% do not own a credit card

c. What is the probability that in a random sample of 500 adults, between 25% and 30% do not own a credit card?

Thank you!