There are 12 agents in one office of a certain real estate firm. Much of the business in this office is conducted by taking a prospective customer out to view a particular property. The time to drive to and view a property is normally distributed and averages 47.3 minutes with a standard deviation of 11.7 minutes. Past studies have shown that twenty-six (26) percent of customers that visit properties with an agent will eventually buy a property being shown by that agent. On average each agent visits 3.6 properties a day, with a standard deviation of 1.9 visits. All of the above activities are independent of each other.

a) What is the probability that an agent will visit at least 7 properties over the next three days?

b) What is the probability that the average time of the next 50 property viewings will be less than 45 minutes?

c) A particular agent currently has 17 prospective customers that are being shown properties for sale. What is the probability that less than 4 of these customers will eventually buy a property being shown by the agent?

d) Eighty-two (82) percent of property visits will take what range of time, centered at the mean.