00:01
We have a coin where the probability of flipping heads is 0 .49.
00:05
We flip the coin 2 ,000 times.
00:09
Okay, so n is 2 ,000, number of independent trials, probability of getting heads, 0 .49.
00:15
So we do have a binomial distribution here.
00:19
We have all requirements.
00:21
Fixed number of independent trials, two outcomes per trial, same probability on each.
00:26
But we want to find the probability of getting between 900.
00:30
And 951, and 996.
00:35
That would take a really long time if we were to say use the binomial formula.
00:41
So we're going to use a normal approximation.
00:45
The normal distribution also has two parameters, but they are the mean and the standard deviation.
00:52
We get these from the binomial.
00:55
So the mean of a binomial, mu, is n p.
00:58
The standard deviation is root n p.
01:04
So the mean is going to be 980.
01:08
Standard deviation is root 499 .8.
01:17
And i am going to leave that in a zax value, just because i don't like rounding errors.
01:23
It's about 22 .4 though.
01:28
Okay.
01:33
So now we have the parameters for our normal distribution.
01:38
So surely we can just go ahead, draw it out, there it is, and we want between 9504.
01:47
Which is below the mean, and 996, which is above the mean.
01:53
So we just find this area and we have it, right? well, there's one last step that we have to do before we just dive in and solve this normal question.
02:03
And that step is called continuity correction.
02:13
So the binomial distribution is discrete.
02:19
If i zoom in on this bit here, the binomial looks like this.
02:23
It's a series of rectangles.
02:25
Each rectangle represents.
02:26
A whole number.
02:29
So i'll say this is 950, 951, 952.
02:34
The normal distribution, however, is continuous.
02:37
It just cuts right through.
02:39
So if i'm saying at least 951, i start here and i go this way right.
02:45
But that's not the most accurate way to approximate.
02:49
It's much more accurate if you cut one of these rectangles in the middle...