6. A company which operates a chain of lunchrooms plans to install a new unit in either of two locations. The company figures that the probability of a unit's being successful in location 1 is 75% and that, if it is successful, it will make an annual profit of $4,000. If it is not successful, however, the company will lose $1.000 a year. The probability of a unit's succeeding in location 2 is only 50%, but if it does succeed the annual profit will be $6,000. If it does not succeed in location 2, the annual loss will be $1,200. (a) Where should the company locate the new unit so as to maximize its expectation? (b) Suppose that the probability of success in location 2 were 62.5%, would that affect the company's decision? 7. Although they have no commercials, public television stations periodically conduct cam- paigns during which programming is occasionally interrupted by appeals for subscriber donations. A local public television station has found that, during these breaks, the number of calls averages 3 per minute. It has recently upgraded the switchboard so it can handle as many as 5 calls per minute. The station is now in the middle of a program break. What is the probability that the switchboard will be overloaded during the next minute? . It has been estimated that about 30% of families with an annual income of $100,000 or more own savings bonds. What is the probability that exactly three of a randomly selected group of five families own savings bonds? How many of the five families do we expect will own savings bonds? 6. A company which operates a chain of lunchrooms plans to install a new unit in either of two locations. The company figures that the probability of a unit's being successful in location 1 is 75% and that, if it is successful, it will make an annual profit of $4,000. If it is not successful, however, the company will lose $1.000 a year. The probability of a unit's succeeding in location 2 is only 50%, but if it does succeed the annual profit will be $6,000. If it does not succeed in location 2, the annual loss will be $1,200. (a) Where should the company locate the new unit so as to maximize its expectation? (b) Suppose that the probability of success in location 2 were 62.5%, would that affect the company's decision? 7. Although they have no commercials, public television stations periodically conduct cam- paigns during which programming is occasionally interrupted by appeals for subscriber donations. A local public television station has found that, during these breaks, the number of calls averages 3 per minute. It has recently upgraded the switchboard so it can handle as many as 5 calls per minute. The station is now in the middle of a program break. What is the probability that the switchboard will be overloaded during the next minute? . It has been estimated that about 30% of families with an annual income of $100,000 or more own savings bonds. What is the probability that exactly three of a randomly selected group of five families own savings bonds? How many of the five families do we expect will own savings bonds