a firm that sells software services has been piloting a new product and has records of $500$ customers who has been piloting a new product and has records of is the estimated gross pre either bought the services or decided not to$.$ The target value about $$2128.$ Hows profit from each sale $($excluding sales costs$).$ The global mean is it comes to $$2500$ for developed a predictive of the $500$ customers $($whether they buy or not$).$ The firm future. The cumulative gadel in hopes of being able to identify the top spenders in the in Figure $5\mathrm{.}14.$

FIGURE $5\mathrm{.}14$ CUMULATIVE GAINS AND DECILE$-$WISE LIFT CHARTS FOR SOFTWARE SERVICES PRODUCT SALES $($HOLDOUT SET$)$

a$.$ If the company begins working with a new set of $1000$ leads to sell the same services, similar to the $500$ in the pilot study $($except the company has not tried to sell the services to the new leads before$),$ without any use of predictive modeling to target sales efforts, what is the estimated gross profit?

b$.$ If the firm wants the average gross profit on each sale to roughly double the sales effort cost and applies an appropriate threshold with this predictive model to a new set of $1000$ leads, how far down the new list of $1000$ should it proceed $($how many deciles$)?$

c$.$ Still considering the new list of $1000$ leads, if the company applies this predictive model with a lower threshold of $$2500,$ how far should it proceed down the ranked leads, in terms of deciles?