Question

13. (21) Florida reports a 30% recidivision rate, that is, 30% of prisoners released from prison return to prison within 3 years of their release. A random sample of eight prisoners who were released three years ago is selected. Of interest is how many of those selected were returned to prison a. In words, describe the random variable X b. What are the possible values of X? c. Find the probability that exactly five were returned to prison. d. Find the probability that at least sik were returned to prison. Is this unusual? Explain.

Answer 1

Given quection have two outcome that is prisoner release from prison and again return in prison within 3 years or he is not return in prison within 3 year.

given case follow all the assumpion of binomial distribution.prisoner release from prison and again return in prison within 3 years.

a) here Random variable x is our success and in our case success is "prisoner release from prison and again return in prison within 3 years.".

b)value of x is 0,1,2,3,4,5,6,7,8.

c) prob that 5 will return to the prison.

p= 0.30 (given)

q =1-p = 0.70.

n= 8 (given).

now,

P( x= 5 ) = nCx * P^x * (1 – P)^n – x

=8C5 * 0.30^5 * (1 – 0.30)^8 – 5

=0.0467

d) at least 6 will return to the prison. It measn the probablity that 6, 7 or 8 prisoner will return to the prison.

p(x>=6) = (8C6 * 0.30^6 * (1 – 0.30)^2) + (8C7 * 0.30^7 * (1 – 0.30)^1) + (8C8* 0.30^8 * (1 – 0.30)^0)

= 0.01129.

this is not unusul because probabilty itself tells that there may chances that out of 1000 xuch type of case will happen 11 times.

THANKS...