NEED TO SHOW ALL WORK TO RECEIVE POINTS For a Geometric Dist

NEED TO SHOW ALL WORK TO RECEIVE POINTS!

For a Geometric Distribution: m = 1/p and s =

1.) P = (0.6)(0.6)(0.6)(0.4) = 0.0864

2.) 1/0.4 = 2.5 = 3 People

3.) s.d = sqrt((1-0.4)/0.4^2) = 1.9365

4.) n = 5, binomial distribution, p = 0.4

P(0) = (0.6)^5 = 0.07776

5.) P(atleast one) = 1-P(none) = 1 - P(0) = 1 - 0.07776 = 0.92224

6.) n = 15, p = 0.4

Binomial distribution

P(8) = 15C8*(0.4)^8(0.6)^7 = 0.118056

7.) P(atleast 12) = P(12) + P(13) + P(14) + P(15)

= 15C12*(0.4)^12(0.6)^3 + 15C13*(0.4)^13(0.6)^2 + 15C14*(0.4)^14(0.6) + (0.4)^15

= 0.001928

8.) P(no more than 3) = (0.6)^15 + 15C1*(0.4)^1(0.6)^14 + 15C2*(0.4)^2(0.6)^13 + 15C3*(0.4)^3(0.6)^12

= 0.090502

9.) P(4 or more) = 1 - P(no more than 3) = 1 - 0.090502 = 0.9095

10.) Expected number = np = (15)*(0.4) = 6

11.) P(7) + P(8) = 15C7*(0.4)^7(0.6)^8 + 15C8*(0.4)^8(0.6)^7 = 0.29514

12.) s.d = sqrt(n*p*(1-p)) = sqrt(15*0.4*0.6) = 1.8974