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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?
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.
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