00:01
In this question, we are given 40 % of students who enter a local community college, that freshmen will go on to graduate, and then freshmen are randomly selected.
00:12
Then let x be the number of freshmen out of this 10 who go on to graduate.
00:17
Now, x follows the binomial distribution.
00:20
You can see there are four criteria here.
00:23
First criteria, the number of trials, n, is fixed at identical.
00:27
Since there are 10 freshmen, there will be 10 trials, so n is equal to 10.
00:31
In this trial is independent.
00:35
We are to assume that these 10 freshmen, they go on to graduate or does not go on to graduate independently.
00:43
So the second and the first criteria fulfilled.
00:45
Third criteria, each trial results in one outcome, success and failure.
00:49
So in this case, the success is the person go on to graduate, failure will be he or she did not graduate.
00:57
Third criteria is fulfilled and the last criteria, the probability of success p remains the same from trial.
01:03
Trial to trial, that is probability that the person graduate, that's the success and that's 40 % or 0 .4.
01:14
So p is 0 .4 and this is constant for each of this freshman.
01:22
So criteria 4 is fulfilled.
01:25
So x follows the binomial distribution and is 10, p is 0 .4.
01:30
Probability x equals to r when r is the number of freshmen out of 10, we'll go on to graduate, that would be then choose r, 0 .4 to power r, and 1 minus 0 .4 is 0 .6 to the power 10 minus r...