Respuesta :
Answer:
The probability that more than 5 parolees out of 15 that return to prison within 3 years is 0.2784.
Step-by-step explanation:
The random variable X be the number of parolees that return to prison within 3 years.
The probability of occurrence of the random variable X is, p = 0.30.
A random sample of n = 15 prisoner are selected.
It is assumed that whether or not one prisoner returns to prison is independent of whether any of the others return to prison.
The random variable X follows a binomial distribution with parameters n = 15 and p = 0.30.
Compute the probability that more than 5 parolees out of 15 that return to prison within 3 years as follows:
[tex]P(X>5)=1-P(X\leq 5)[/tex]
[tex]=1-\sum\limits^{5}_{0}{{15\choose x}(0.30^{x}(1-0.30)^{15-x}}\\\\=1-[0.00475+0.03052+0.09156+0.17004+0.21862+0.20613]\\\\=0.27838\\\\\approx 0.2784[/tex]
Thus, the probability that more than 5 parolees out of 15 that return to prison within 3 years is 0.2784.
