Greg must sell three more cars this month tomeet his quota. Tonight he has after

Question

Greg must sell three more cars this month tomeet his quota. Tonight he has after-dinner appointments withfive prospective customers, each of whom happensto be interested in a different car. If he has a30% chance of success with each customer, what isthe probability that he'll meet his quota by tomorrow morning??Suppose that three of Greg's customers wereinterested in the same car, and that they'll go elsewhere if it hasalready been sold. Would it be appropriate to use the binomialdistribution under these conditions? Why or why not?? Help please!! Greg must sell three more cars this month tomeet his quota. Tonight he has after-dinner appointments withfive prospective customers, each of whom happensto be interested in a different car. If he has a30% chance of success with each customer, what isthe probability that he'll meet his quota by tomorrow morning??Suppose that three of Greg's customers wereinterested in the same car, and that they'll go elsewhere if it hasalready been sold. Would it be appropriate to use the binomialdistribution under these conditions? Why or why not?? Help please!!

Explanation / Answer

to meet the quota greg must sell three or more cars thus he must be able to sell atleast 3 out of the fivecustomers also given that he has 30% chance of success with eachcustomer i.e. the probability tht will be able to sell car to eachcustomer is 0.3 thus n=5,p=0.3 for binomial distn.P(X=x)=C(n,x)px(1-p)n-x we need to find P(X>=3)=)P(X=3)+P(X=4)+P(X=5) P(X>=3)=C(5,3)*0.33*0.72+C(5,4)*0.34*0.7 +C(5,5)*0.35              =10*0.33*0.72+5*0.34+0.35 now binomial distn can be used only if the prob. of oneoutcome is independent of the other thus if all customers (or even two customers) are interestedin the same car then whether one customer will buy a car or no will depend onthe previous customer if the previous customer have bought the car then the customerwont buy as his choice of car is sold thus the occurance is not independent and so under theseconditions it would be inappropriate to use bin. distn. {tht is the reason they have mentioned tht all customers areinterested in different car without the given condition binomial distn cannot beapplied} hope this helps now binomial distn can be used only if the prob. of oneoutcome is independent of the other thus if all customers (or even two customers) are interestedin the same car then whether one customer will buy a car or no will depend onthe previous customer if the previous customer have bought the car then the customerwont buy as his choice of car is sold thus the occurance is not independent and so under theseconditions it would be inappropriate to use bin. distn. {tht is the reason they have mentioned tht all customers areinterested in different car without the given condition binomial distn cannot beapplied} hope this helps

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