00:01
In this question, we are given in a report that 40 % of policyholders, 55 years or older, submit a claim during the year.
00:09
Now, 15 policy holders are randomly selected.
00:13
I'm going to let x be the number of policy or holders of this 15, who have filed a claim within the last year.
00:20
Now, x actually follows the binomial distribution.
00:23
Let's take a look how it follows the binomial distribution.
00:26
For binomial distribution, there are four criteria.
00:29
First criteria, the number of trials and is fixed and are identical.
00:33
Now in this case, we have 15 policyholders, so end is 15 and that's fixed.
00:39
And the trial is that we are looking for each policyholder, whether they have filed a claim within the last year.
00:46
So these trials are identical.
00:50
So first criteria is fulfilled.
00:52
Second criteria, each trial is independent.
00:55
Now, each policyholder, whether they file a claim or not, within the last year, is independent each other.
01:01
So second criteria is fulfilled.
01:04
The criteria, each trial results in one or two outcomes, success and failure.
01:08
So for each policyholder, the success would be he or she has fought a claim and the failure would be he or she has not filed a claim.
01:18
So criteria three is fulfilled.
01:20
Criteral four, the probability of success denoted by p, remains the same from trial to trial.
01:27
Now, in this case, the probability of success would be...