Answer the following questions. a. Suppose that 50% of the U.S. citizens is under 30 years old (i.e., the median age of the U.S. citizens is 30). If a survey of 500 randomly selected U.S. citizens is conducted, what is the probability at most 240 of them will be under 30 years old? (3 pts) b. Heidi prepares for an exam by studying a list of 15 problems. She can solve nine of them. For the exam, the instructor selects seven questions at random from the list of fifteen. What is the probability that Heidi can solve all seven problems on the exam? (2 pts) c. About 70% of Florida residents believe that Florida is a nice place to live. Suppose that six randomly selected Florida residents are interviewed. What is the probability that at least one resident does not think that Florida is a nice place to live? (2 pts) d. An interior decorator must furnish two offices. Each office must have a desk, a chair, and a file cabinet and two bookcases. At a local office furniture store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets and 10 models of bookcases, all of which are compatible (Any desk can be matched with any chair, etc.). How many choices does the decorator have if he wants to select two desks, two chairs, two file cabinets and 4 bookcases if he doesn't want to select more than one of any model? (2 pts) e. A professor has received a grant to travel to an archaeological dig site. The grant includes funds for three graduate students to accompany the professor. If there are six graduate students available to the professor and all the funds are to be used (i.e., three students will go), how many choices does the professor have? (2 pts) f. Suppose 40% of the students in a certain college are female. Suppose further that 15% of the females and 10% of the males are smokers. What is the probability that a randomly chosen smoker is female? (4 pts)