Story Punle 1 Matthew teaches statistics at a prestigious community college. During his graduate studies, he

was fortunate to be trained in SPSS, a computer software created by IBM for statistical analysis.

He thinks his students could have a better chance of getting jobs in data analysis if they knew

how to work with this software. He decides to have a seminar on an introduction to SPSS.

Unfortunately, his college doesn’t have the funding necessary to support SPSS. So, he reaches

out to IBM directly. After much negotiation, the company offers him access to SPSS for his seminar free of charge if

two conditions are met. First, there must be at least ﬁfty students participating in his seminar,

and each student will get a limited access to the program. Second, he must advertise the

seminar to his colleagues at the college. The company will provide him with twenty free full

access codes to SPSS for instructors at his college but any additional access codes must be

purchased. Matthew, who already has a copy of the software for his personal use, agrees. Matthew wants to meet IBM's conditions. but he doesn’t want to pay for any additional license

access fees. He is also limited by room size so he cannot send out mass emails to all statistics

students. Therefore, he must determine how many invitations he should send out to students

and faculty. Since he is new at the college, he decides to consult with one of his resourceful

colleagues, Mario. After carefully listening to Matthevifs situation, Mario tells him, "I can tell you from my

experience what kind of probabilities you should expect on participation. There is a 60% chance

that a statistic student will show up to your seminar after receiving your invitation. Faculty

members are busier, so only one out of three will show up. Given the room that you are

planning to utilize for your seminar, the probability of having at least ﬁfty students show up is

at most 90%.” Matthew immediately takes out his TI-ail calculator and after a couple of

minutes says, "I know how many seminar invitations I should send out now.” Mario replies, "Are you trying to send out the most number of invitations possible?” Matthew

responds, "Yes, of course. It is my ﬁrst seminar and I want to be on the safe side.” Mario agrees

but asks curiously, “With the information I gave you, I see how you got the number of student

invitations. But how did you work out the number for the faculty invitations?” Matthew responds, "Well, I just made sure that the probability of at most twenty faculty

attending the seminar is very high." Mario asks, "How high?” Matthew replies, "At least 95%,

we statisticians like that one, don’t we?" Mario nods his head in agreement and says, ”Yes, I

see. The problem is solved." They exchange some pleasa ntry and depart. Once Matthew is out of his office, Mario calculates the probability of at least ﬁfty students and

at most twenty faculty showing up to Matthew's seminar after they receive the invitations. He

thinks to himself, ”Matthew is going to be ﬁne.” Find the number of seminar invitations that Matthew will send out to statistics students and

the number of invitations for faculty {or his colleagues). Determine the probability of at least

fiftyr students and at most twenty faculty showing up to Matthew’s seminar under the given

conditions? Do you agree or disagree with Mario’s last thought? Why?