#### sara

##### New Member
Hi,

I would appreciate any input regarding this problem: I showed my effort under each question

A college professor found herself assigned to a committee of 6 people, composed of 4 men and 2 women. the committee had to select 2 officers tocarry out the majority of the administrative work, and it turned out that both of the women were selected. The professor wondered whether this occured through subtle discrimination, so she considered how unlikey such event ( 2 women being selected ) would be if the two officials had been chosen at random from the 6 committee members. suppose that the 6 members are named Alice, Bonnie, Carl, Danny, Evan, and Frank.

1) calculate the sample mean numbers of men in those 25 simulated pairs of officers

answer: 6/25= 0.24=24% ( I used Minitab to simulate my 25 trials: minimum 1, Max 6)

2) calculate the population mean number of men expected among the two officers
mean= population* probability
= 4*0.24 = 0.96
3) How close was your simulation in part (1)to the true answe in part (2)

My simulation is part1 is not close to the true answer in part 2 ( 0.24#0.96)

I hope that I am in the right path.

thanks so much

#### Mean Joe

##### TS Contributor
1) calculate the sample mean numbers of men in those 25 simulated pairs of officers
The sample mean should be a number, rather than a percent; all you have to do is count the number of men in each simulation, and find the average.
e.g. I do 5 simulations and get AB (i.e. Alice & Bonnie are the chairpersons), BC, BE, BC, DA (i.e. Danny & Alice are the chairpersons)
So # of men in each simulation: 0, 1, 1, 1, 1
Thus my sample mean would be 0+1+1+1+1 / 5 = 0.8

2) calculate the population mean number of men expected among the two officers
A couple ways to do this. One way:
There are 15 total possibilities for selecting two chairpersons from 6 people.
# of those possibilities where 0 are men: 1
# of those possibilities where 1 is a man: 8
# of those possibilities where 2 are men: 6

So then the sample mean is (0 * 1) + (1 * 8) + (2 * 6) / 15 = 1.333

3) How close was your simulation in part (1)to the true answe in part (2)
My simulation differed from the true answer by (.8 - 1.333) / 1.333 = 40%

NOTE: Your answers for #1 and #3 are likely to be different, because you were doing 25 simulations rather than just 5. I just meant to show you how you could answer.