00:01
In this question, we're given in the prison system, 61 % of all violent felons are repeat offenders.
00:10
30 violent felons are randomly selected.
00:13
I'm going to let x be the number of violent felons out of these 30 who are repeat offenders.
00:18
So n, the number of trials will be 30 since there are 30 felons.
00:22
And so there will be 30 trials.
00:25
In each trial, we will take a look at whether this felon is a repeat offender or not.
00:30
And p, the probability of success.
00:31
In a single trial in this case is probability of a felon being a repeat offender, there will be 61 % or 0 .61 in decimal.
00:42
So x follows the binomial distribution, n is 30, p is 0 .61.
00:49
Probability x equals to r, where r is the number of violent felons are 30 who are repeat offender.
00:55
That will be 30 choose r, 0 .61 to power r, and 1 minus 0 .61 and 0 .39, to the power of 1 ,000, of 30 minus r.
01:06
Like part a, want to find probability, exactly 17 of them are repeat offenders.
01:12
So we want to look at probability of x equals to 17.
01:15
We can use the formula.
01:17
Just sub 17 into the r.
01:30
We'll get 0 .196, 4 decimal place.
01:38
Or we can use excel.
01:42
So using excel or you can use your calculator that can compute binomial distribution.
01:48
For excel, i will show you for the equal sign here, we'll be using what we call the cumulative is false because this is not cumulative.
02:01
Cumulative will be less than equal.
02:02
That's the cumulative.
02:04
Now if you are using calculator, equal here you'll be using by non -pdf.
02:10
Pdf as in probability distribution function because we want to find the probability at this point, 17.
02:17
Now less than equal, you'll be using cdf, which is the cumulative distribution function.
02:20
Distribution function...