53% of all violent felons in the prison system are repeat offenders. if 43 violent felons...
Homework Answers
a)
p = 0.53
n =43
P ( X = 24 ) = C(43,24) * 0.53^24 * (1-0.53)^19 = 0.1137
b)
| X | P(X) | |
| P ( X = 0) = C (43,0) * 0.53^0 * ( 1 - 0.53)^43= | 0 | 0.0000 |
| P ( X = 1) = C (43,1) * 0.53^1 * ( 1 - 0.53)^42= | 1 | 0.0000 |
| P ( X = 2) = C (43,2) * 0.53^2 * ( 1 - 0.53)^41= | 2 | 0.0000 |
| P ( X = 3) = C (43,3) * 0.53^3 * ( 1 - 0.53)^40= | 3 | 0.0000 |
| P ( X = 4) = C (43,4) * 0.53^4 * ( 1 - 0.53)^39= | 4 | 0.0000 |
| P ( X = 5) = C (43,5) * 0.53^5 * ( 1 - 0.53)^38= | 5 | 0.0000 |
| P ( X = 6) = C (43,6) * 0.53^6 * ( 1 - 0.53)^37= | 6 | 0.0000 |
| P ( X = 7) = C (43,7) * 0.53^7 * ( 1 - 0.53)^36= | 7 | 0.0000 |
| P ( X = 8) = C (43,8) * 0.53^8 * ( 1 - 0.53)^35= | 8 | 0.0000 |
| P ( X = 9) = C (43,9) * 0.53^9 * ( 1 - 0.53)^34= | 9 | 0.0000 |
| P ( X = 10) = C (43,10) * 0.53^10 * ( 1 - 0.53)^33= | 10 | 0.0001 |
| P ( X = 11) = C (43,11) * 0.53^11 * ( 1 - 0.53)^32= | 11 | 0.0002 |
| P ( X = 12) = C (43,12) * 0.53^12 * ( 1 - 0.53)^31= | 12 | 0.0005 |
| P ( X = 13) = C (43,13) * 0.53^13 * ( 1 - 0.53)^30= | 13 | 0.0014 |
| P ( X = 14) = C (43,14) * 0.53^14 * ( 1 - 0.53)^29= | 14 | 0.0033 |
| P ( X = 15) = C (43,15) * 0.53^15 * ( 1 - 0.53)^28= | 15 | 0.0073 |
| P ( X = 16) = C (43,16) * 0.53^16 * ( 1 - 0.53)^27= | 16 | 0.0144 |
| P ( X = 17) = C (43,17) * 0.53^17 * ( 1 - 0.53)^26= | 17 | 0.0258 |
| P ( X = 18) = C (43,18) * 0.53^18 * ( 1 - 0.53)^25= | 18 | 0.0420 |
| P ( X = 19) = C (43,19) * 0.53^19 * ( 1 - 0.53)^24= | 19 | 0.0624 |
| P ( X = 20) = C (43,20) * 0.53^20 * ( 1 - 0.53)^23= | 20 | 0.0844 |
| P ( X = 21) = C (43,21) * 0.53^21 * ( 1 - 0.53)^22= | 21 | 0.1042 |
| P ( X = 22) = C (43,22) * 0.53^22 * ( 1 - 0.53)^21= | 22 | 0.1175 |
| P ( X = 23) = C (43,23) * 0.53^23 * ( 1 - 0.53)^20= | 23 | 0.1210 |
| P ( X = 24) = C (43,24) * 0.53^24 * ( 1 - 0.53)^19= | 24 | 0.1137 |
| P ( X = 25) = C (43,25) * 0.53^25 * ( 1 - 0.53)^18= | 25 | 0.0975 |
= 0.7957
c)
| X | P(X) | |
| P ( X = 0) = C (43,0) * 0.53^0 * ( 1 - 0.53)^43= | 0 | 0.0000 |
| P ( X = 1) = C (43,1) * 0.53^1 * ( 1 - 0.53)^42= | 1 | 0.0000 |
| P ( X = 2) = C (43,2) * 0.53^2 * ( 1 - 0.53)^41= | 2 | 0.0000 |
| P ( X = 3) = C (43,3) * 0.53^3 * ( 1 - 0.53)^40= | 3 | 0.0000 |
| P ( X = 4) = C (43,4) * 0.53^4 * ( 1 - 0.53)^39= | 4 | 0.0000 |
| P ( X = 5) = C (43,5) * 0.53^5 * ( 1 - 0.53)^38= | 5 | 0.0000 |
| P ( X = 6) = C (43,6) * 0.53^6 * ( 1 - 0.53)^37= | 6 | 0.0000 |
| P ( X = 7) = C (43,7) * 0.53^7 * ( 1 - 0.53)^36= | 7 | 0.0000 |
| P ( X = 8) = C (43,8) * 0.53^8 * ( 1 - 0.53)^35= | 8 | 0.0000 |
| P ( X = 9) = C (43,9) * 0.53^9 * ( 1 - 0.53)^34= | 9 | 0.0000 |
| P ( X = 10) = C (43,10) * 0.53^10 * ( 1 - 0.53)^33= | 10 | 0.0001 |
| P ( X = 11) = C (43,11) * 0.53^11 * ( 1 - 0.53)^32= | 11 | 0.0002 |
| P ( X = 12) = C (43,12) * 0.53^12 * ( 1 - 0.53)^31= | 12 | 0.0005 |
| P ( X = 13) = C (43,13) * 0.53^13 * ( 1 - 0.53)^30= | 13 | 0.0014 |
| P ( X = 14) = C (43,14) * 0.53^14 * ( 1 - 0.53)^29= | 14 | 0.0033 |
| P ( X = 15) = C (43,15) * 0.53^15 * ( 1 - 0.53)^28= | 15 | 0.0073 |
| P ( X = 16) = C (43,16) * 0.53^16 * ( 1 - 0.53)^27= | 16 | 0.0144 |
| P ( X = 17) = C (43,17) * 0.53^17 * ( 1 - 0.53)^26= | 17 | 0.0258 |
| P ( X = 18) = C (43,18) * 0.53^18 * ( 1 - 0.53)^25= | 18 | 0.0420 |
| P ( X = 19) = C (43,19) * 0.53^19 * ( 1 - 0.53)^24= | 19 | 0.0624 |
| P ( X = 20) = C (43,20) * 0.53^20 * ( 1 - 0.53)^23= | 20 | 0.0844 |
| P ( X = 21) = C (43,21) * 0.53^21 * ( 1 - 0.53)^22= | 21 | 0.1042 |
| P ( X = 22) = C (43,22) * 0.53^22 * ( 1 - 0.53)^21= | 22 | 0.1175 |
| P ( X = 23) = C (43,23) * 0.53^23 * ( 1 - 0.53)^20= | 23 | 0.1210 |
= 1 - 0.5846
= 0.4154
d)
| P ( X = 17) = C (43,17) * 0.53^17 * ( 1 - 0.53)^26= | 17 | 0.0258 |
| P ( X = 18) = C (43,18) * 0.53^18 * ( 1 - 0.53)^25= | 18 | 0.0420 |
| P ( X = 19) = C (43,19) * 0.53^19 * ( 1 - 0.53)^24= | 19 | 0.0624 |
| P ( X = 20) = C (43,20) * 0.53^20 * ( 1 - 0.53)^23= | 20 | 0.0844 |
| P ( X = 21) = C (43,21) * 0.53^21 * ( 1 - 0.53)^22= | 21 | 0.1042 |
| P ( X = 22) = C (43,22) * 0.53^22 * ( 1 - 0.53)^21= | 22 | 0.1175 |
| P ( X = 23) = C (43,23) * 0.53^23 * ( 1 - 0.53)^20= | 23 | 0.1210 |
| P ( X = 24) = C (43,24) * 0.53^24 * ( 1 - 0.53)^19= | 24 | 0.1137 |
| P ( X = 25) = C (43,25) * 0.53^25 * ( 1 - 0.53)^18= | 25 | 0.0975 |
= 0.7685
Please revert back in case of any doubt.
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