Question

50% of all violent felons in the prison system are repeat offenders. If 37 violent felons are randomly selected, find the probability that  

a. Exactly 16 of them are repeat offenders. 
b. At most 19 of them are repeat offenders. 
c. At least 19 of them are repeat offenders. 
d. Between 12 and 19 (including 12 and 19) of them are repeat offenders.

Answer 1

As pen given data p=0.5 ,q=0.5 n=37 Binomial fremulce Pcx=x) = no ncc optoqu-x. Exactly 16 of them 16 of them case repeab offenders. Porn 6) = Po=16= 37c Poc=16) €20.60.5346.60.53446 0.0937 b et most is of them are repent offender. Pra <19)=P(0) +P01] + .. +Plug) - =376:10.51960.337.....437.co.s)? 60.5337-19 ciuse Calculation to find viehee) Pas 19) = 0.6286 are sepeut offender at least Ig of them Proy 1g) = P(ig)+plQo] + ... + P237) -37 (0.5):(0.5) ? ;.co.sjo 34 PO) 19)-0.5000

an 12 and 19) PC IQS X319) - P112) + P113)+ - + prig) +370.cous)?(0.53 નર + 12. 3719 + 3+ 19 er(0.5)':(0.5% cuse Calculates to find vuhre) PC ia sacs19) ► 0.6186