Email #1
Email from administrator to research staff
January 15, 10:46 a.m.
Yesterday was the deadline for our receipt of completed surveys from doctors who were invited to participate in the Medical Practice Priorities Survey. Did we get enough returns from this original group of invitees to get reliable statistics? Do we need to invite additional participants?
Email #2
January 15. 11:12 a.m.
Altogether we got exactly 350 actual completions. We need at least 700 and were hoping for even more, so we plan to invite a second group to participate. Both the results from this first group and other research indicates that with this type of survey and this type of participants there is about a 40 percent probability that any given invitee will submit the completed survey in the time we’ll allow. (Obviously that doesn’t mean that if we invited 1,000 we’d necessarily get at least 400, so we need to think in terms of the risks of getting too few returns or exceeding the budget.) All of the participants who submitted their surveys by the deadline will get the $50 payment we promised. What is our total budget for compensation to participants?
Email #3
January 15, 1:54 p.m.
The budget we allocated for compensation to those who complete and submit the Medical Practice Priorities Survey is $45,000. We will honor our commitment to pay $50 to each participant—in the second group as well as the first--who completes the survey and submits it by the deadline we specify when we invite them to participate. However, we will need to try not to exceed the total amount that is budgeted for this purpose.
Consider each of the following statements. Does the information in the three emails support the inference as stated?
YesNo
The administrator is unwilling to invite as many participants in the second group as were invited in the first group.
The project coordinator does not expect to be able to meet the goal for numbers of completed surveys received.
The administrator is willing to accept some risk of exceeding the budget for compensating participants.
The administrator and the project coordinator disagree about how many people should be invited to participate in the second group.
Suppose that the total number of invitees in the second group is 560. Than, if all of the information in the three emails is accurate, the probability that the budget for compensating participants will be exceed is nearest to:
a)1.0
b)0.8
c)0.5
d)0.2
e)0.0
题目翻译：
邮件1
行政人员发给研究人员
1月15日，上午10:46
昨天是收到受邀的医生参与医学实践重点调查完成调查的截止日期，我们已经从这个原始的受邀者那里得到了足够的回复，从而能够得到更可信的数据了吗?我们还需要邀请额外的参与者吗?
邮件2
项目协调人员回复行政人员的1月15日上午10：46的邮件
1月15日，上午11:12
我们总共收到了350份完成的调查。我们至少需要700份甚至更多，所以我们打算邀请第二组来参与调查。第一组的调查结果和其他的调查都表明了用这种形式的调查，邀请这方面的参与者，他们中会有40%的可能会在我们允许的时间范围内提交完成的调查。(很显然这并不意味着我们邀请1000个参与者，我们就一定会得到至少400份回复，所以我们需要考虑得到太少的回复的风险或者超出预算的风险。)我们承诺的所有在截止日期之前提交完成的调查的参与者将会的到50美元。我们对参与者的补偿的预算是多少呢?
邮件3
行政人员回复项目协调人员的1月15日上午11:12的邮件
1月15日，下午1:54
我们分配的补偿完成并提交医学实践重点调查的人的预算是45000美元。我们将尊重我们的承诺给每个参与者50美元---第一组与第二组一样---那些在我们邀请他们参与时强调的截止日期之前完成并提交了调查的参与者。然而，我们需要尽量不要超过预算。
考虑一下的每一个描述。三封邮件里面的信息支持下面描述的推断吗?
是否
行政人员不愿意在第二组邀请与第一组同样多的参与者。
项目协调人员并不指望能够达到收到完成的调查的数量的目标。
行政人员愿意接受超出补偿参与者的预算的风险。
行政人员和项目协调人员在关于多少人应该再第二组被邀请参与调查的问题意见不一致。
假设第二组邀请的参与者的总数为560。如果三封邮件上的信息是准确的，超出补偿参与者的预算的可能性最接近于：
a)1.0
b)0.8
c)0.5
d)0.2
e)0.0
题目解析：
邮件2中项目协调人员说已经收到350个回复，但是至少需要700个回复，第二组应该与第一组数量相当或者超过第一组，而行政人员并没有表示反对的态度。所以答案为否。
邮件2种项目协调人员说他们需要700份甚至更多而现在只有350份，然后又提到打算再邀请一组的参与者并给予50美元的报酬等，都表明了他期望能够达到收到完成了的调查的数量的目标。所以表述是没有根据的，答案为否。
行政人员说要尽量不要超出预算，但是他仍然给了45000的预算，表明他是愿意接受这个风险从而得到参与者提交的调查的。
行政人员和项目协调人员并没有在邮件中针对在第二组种邀请多少参与者产生分歧，只是在讨论参与者不够数量以及给予参与者报酬的预算的问题。
第二组受邀请的人数为560人，根据邮件，有大约40%会提交完成的调查，也就是560*0.4=224人会得到报酬，为224*50=11200美元。第一组完成并提交调查的人数为350人，所需的报酬为350*50=17500美元。两组总共所需要的报酬为11200+17500=28700美元，小于预算的45000美元，没有超出预算。所以超出预算的可能性最接近于0。
