00:01
It's stated in this question that 1 out of 390 loans made by mammon bank have defaulted.
00:06
So for any randomly selected loan at this bank, the probability of default is 1 out of 390.
00:13
We want to find, we're interested in finding the probability that 5 or more out of 350 will default.
00:21
So let's define a random variable x as the number of loans in the sample of 350 that default.
00:28
So in this situation, x is actually a binomial random variable, assuming that the outcomes for the 350 loans are all independent.
00:42
And the binomial distribution has two parameters, the number of trials and the probability of success, or in this case a default, on each trial.
00:55
And for the binomial distribution, when the number of trials is very large, for example example, more than 100, and the probability of success on each trial is very small, in this case 1 out of 390 is very small, then you can use the poisson approximation to the binomial distribution.
01:14
So n is at least 100 here, and another rule of thumb is if n times p is at most 10.
01:27
So for us, n is 350, and n times p is approximately 0 .9.
01:38
So therefore, therefore we can use the poisson approximation to the binomial distribution...