Question

The City of Hamilton forms a committee to improve low-income well-being in the city. A
committee of 5 people is to be formed from 11 ward councillors and 8 nonprofit representatives. If
they were picked at random...
1. Calculate the expected number of nonprofit representatives on this committee. [2]
2. Create a hypergeometric distribution graph, checking for number of nonprofit
representatives. Include the table with the graph. (To save yourself time, check back in the
lesson for the formulas to drop in your spreadsheet!) [3]

Answer 1

C_(11+8),5 = 11628 - possible committees

committe with 5 ward councillors

С_11,5=462

committe with 4 ward councillors and 1 nonprofit representatives

С_11,4*С_8,1=330*8=2640

committe with 3 ward councillors and 2 nonprofit representatives

С_11,3*С_8,2=165*28=4620

committe with 2 ward councillors and 3 nonprofit representatives

С_11,2*С_8,3=55*56=3080

committe with 1 ward councillors and 4 nonprofit representatives

С_11,1*С_8,4=11*70=770

committe with 5 nonprofit representatives

С_8,5=56

E=(0*462+1*2640+2*4620+3*3080+4*770+56*5)/11628=24480/11628=2.1

p(0)=462/11628 =0.0397

p(1)=2640/11628 =0.227

p(2)=4620/11628 =0.397

p(3)=3080/11628 =0.2648

p(4)=770/11628 =0.066

p(5)=56/11628 =0.0048

p(0) p(1) p(2) p(3) p(4) p(5)

0.0397 0.227 0.397 0.2648 0.066 0.0048

graph: