A major obstacle to developing sales plans and their respective control procedures is the lack of meaningful data for decision making. The use of stochastic models in sales management can help improve short-term sales strategies and procedures that will aid in the long-term development of effective salespeople. Thus, a well-known insurance company in the country hires him to provide a mathematical model to help them analyze their telephone sales. You analyze the historical data and find the following:  In each call the interest of the person can be identified, this term denotes the propensity to buy as perceived by the seller when making a call. You decide to classify that interest as low, medium, and high.  When interest is low, there is only a 5% chance of making a sale. When the interest is medium, there is a 15% probability. This probability increases by 5% when moving to the last category.  When interest is low, there is a 45% chance that a sale will not be made. There is a high quantitative jump when going to a medium interest, since this probability decreases to 10% and then ends at 5% when the interest is high.  As several calls are made to the same client, it is identified that, if their interest is low, it will remain so with a 10% probability. The chances of going to medium or high interest if you previously had low interest are the same.  If the interest of a client was intermediate in a previous call, in the next one it remains the same with a 25% probability, the interest decreases with a 35% possibility and 15% of the clients go to high interest.  When an external client has a high interest in the insurance package that is offered, in a next call they keep it with a 15% chance, but they have the same probability of going down to the medium or low interest categories. Answer the following questions (use three decimal places and a period as the decimal point): Considering that the client can change his opinion several times to less favorable interest and lost sales, how many calls should be made to consolidate a sale if the interest of the person is high?

It is anticipated that a salesperson person needs to spend 12 minutes per call in the event that the client person shows high interest. How much time on average do you really need to invest in this case to CONSOLIDATE a sale? (in minutes)

As a new policy, the company decides that if the probability of making a sale increases by at least 10%, a second call must be made. How much is the probability of sales increasing with a second call if the person showed low interest at first? (If there is no increase, put a zero).

After three calls, what is the probability of making a sale if the customer's initial interest was low?

What is the expected number of times the customer will show low interest if they previously showed high interest?

Cul es la cantidad esperada de veces que el cliente va a mostrar un inters medio antes de que se consolide una venta?

What is the expected number of times the customer will show average interest before a sale is consolidated?

What is the probability of making a sale if the interest shown by the customer is medium?

What is the probability of not making a sale if the interest shown by the customer is medium?