Solve it step by step must be very organized and detailed responses and answer the question effectively! must correlate to Finance 230 formulas. Thank You

1. The records of a department store show that 20% of its customers who make a purchase return the merchandise in order to exchange it. In the next six purchases, a. what is the probability that three customers will return the merchandise for exchange? b. what is the probability that four customers will return the merchandise for exchange? what is the probability that none of the customers will return the merchandise for c. exchange? (Hint: Binomial probability distribution) 2. An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch. What is the probability that during the next week a. exactly seven claims will be filed? b. no claims will be filed? c. less than four claims will be filed? d. at least eighteen claims will be filed? (Hint: Poisson probability distribution) 3. Z is a standard normal variable. Find the value of z in the following. a. The area between 0 and z is 0.4678. b. The area to the right of z is 0.1112. c. The area to the left of z is 0.8554 d. The area between z and z is 0.754. e. The area to the left of z is 0.0681. f. The area to the right of z is 0.9803. 4. In 2014, the per capita consumption of soft drinks in the United States was reported to be 42.1 gallons. Assume that the per capita consumption of soft drinks in the United States is approximately normally distributed with a mean of 42.1 gallons and a standard deviation of 13 gallons. a. What is the probability that someone in the United States consumed more than 60 gallons of soft drinks in 2014? b. What is the probability that someone in the United States consumed between 15 and 30 gallons of soft drinks in 2014? c. What is the probability that someone in the United States consumed less than 15 gallons of soft drinks in 2014 ? d. Ninety-nine percent of the people in the United States consumed less than how many gallons of soft drinks