A recent poll of over 2,000 adults was designed to answer the question "Are adults superstitious?" One survey item concerned the phrase "see a penny, pick it up, all day long you'll have good luck." The poll found that just one-forth of adults (25%) believe finding and picking up a penny is good luck. Consider a random sample of 15 adults and let x represent the number who believe finding and picking up a penny is good luck. Complete parts a though f below. O D. A success is an adult who believes finding and picking up a penny is bad luck. b. Explain why x is (approximately) a binomial random variable. A. Sampling 2000 adults is equivalent to performing a coin-toss type experiment. The survey only contains two options and each option can be considered a success or a failure. The survey does not change from person to person and each survey response is independent of each other. O B. Binomial random variables are always obtained through sampling. The survey only contains two options and each option can be considered a success or a failure. The survey changes from person to person and each survey response is independent of each other. O C. Binomial random variables are always obtained through sampling. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey does not change from person to person and each survey response is dependent of all the previous responses. O D. Sampling 2000 adults is equivalent to performing a dice-roll type experiment. The survey contains at least three options, so one of the options can be considered a success while the others are failures. The survey changes from person to person and each survey response is independent of each other. c. Give the value of p for this binomial experiment. p= 0.25 (Round to two decimal places as needed.) d. Find P(x<5). P(x<5) = 0.687 (Round to three decimal places as needed.) e. Find P(x= 6). P(x= 6) = (Round to three decimal places as needed.)