00:01
Okay, and your question talking about policyholders submitting claims, you're told that about 40 % submit a claim.
00:10
And now what we've done is we've randomly selected 15 policyholders, and we want to answer these questions.
00:17
How many would you expect to have filed a claim? what this is called is an expected value question.
00:25
They either submitted a claim or they didn't.
00:30
So i'm finding these formulas under what are called binomial distributions.
00:35
And all i'm looking at here would be n is the number of randomly selected participants, in this case 15, times the probability or the proportion that they submit a claim.
00:49
So all we would have to do for this expected value would be to take 15 times 0 .4, and that's going to be six.
00:59
We would expect to see six of the policyholders that we selected out of the 15 to have submitted a claim.
01:09
Now the rest of these things, we're looking at binomial distributions.
01:13
We're looking for the probability of a certain number of successes here in part b.
01:20
And there's a specific formula that i can use.
01:23
Yes, we can use technology for this one, but since we're finding a specific number of successes, 10, we could do this with the formula by hand somewhat.
01:34
What i have here is the formula for the situation.
01:39
We would have n, which would stand for the number of trials, in this case, 15 people.
01:44
And we're looking for how many combinations of 10, x is going to stand for 10.
01:49
Then we take the probability of the situation, submitting a claim, raised to the 10 that we want to submit a claim.
01:58
And then the other five people selected would not have submitted a claim so we would do the complement probability raised to the fifth power 15 minus 10.
02:11
So how this looks with the numbers would be 15c10 times 0 .4 raised to the 10th power times 0 .6 raised to the fifth power.
02:27
And the c symbol here stands for combinations.
02:31
It's basically saying how many different ways could we select groups of 10 out of those 15? now, you'd still need a calculator to probably do that.
02:42
So i'm going to type that in.
02:54
I'm trying.
02:55
It's not working.
03:00
Okay, so there are 3 ,000 and three different ways we could pick groups of 10.
03:08
That's all i've typed into calculator so far.
03:10
Now i'm going to take that times these two values, which is a very tiny number, which i'm not going to write out.
03:25
So i'm just going to put that in that spot and then multiply it by 3 ,003.
03:34
Then i end up with 0 .0 .245, or you can say about 2 .45%.
03:53
Now these next two questions, it just doesn't make sense to approach them by using the formula.
03:59
More than likely you're using a technology here because we would have to do this formula for 10.
04:05
We would have to do it for 11...