It is claimed that [tex]$46 \%$[/tex] of all violent felons in the prison system are repeat offenders. Based on this, if 35 violent felons are randomly selected, find the probability that:
a. Exactly 15 of them are repeat offenders.
[tex]\[ P(X = 15) = \square \][/tex]
b. At most 16 of them are repeat offenders.
[tex]\[ P(X \leq 16) = \square \][/tex]
c. At least 15 of them are repeat offenders.
[tex]\[ P(X \geq 15) = \square \][/tex]
d. Between 12 and 18 (including 12 and 18) of them are repeat offenders.
[tex]\[ P(12 \leq X \leq 18) = \square \][/tex]
e. The mean of this distribution is
[tex]\[ \mu = \square \][/tex]
f. The standard deviation of this distribution is
[tex]\[ \sigma = \square \][/tex]