00:01
So you have several questions that you've asked here, and they're all basically the same type, and it's using a normal approximation to a binomial.
00:08
So i'm going to go through the first three.
00:09
So on the first problem, you have that 18 % of people have used a hospital er room, an emergency room, in the past year.
00:20
And a sample of 140 people were asked, and x is going to stand for the number of people who used the emergency room in the, that sample of 140.
00:32
And so the mean for this setting for a binomial a polynomial distribution is n times p.
00:39
So 0 .18 times 140 gives us this 25 .2 as the mean.
00:45
And our standard deviation is the square root of n times p times 1 minus p and that comes out to be about 4 .5.
00:53
Now we want to use the continuity correction and we want to find the likelihood that fewer than 222 of those 140 end up going to the er room.
01:04
So when we're doing the continuity correction, we want strictly less than.
01:10
And so we know we could say that means 21.
01:14
It's less than or equal to 21.
01:16
But the continuity correction is to bump it up a half a unit.
01:20
So right here is using the continuity correction, changing that less than 22 to 20 less than or equal to 21 .5.
01:28
And then we convert it to a z value using that normal approximation.
01:32
So the number minus the mean divided by the standard deviation.
01:36
And i round that up to two places so i could use my table.
01:39
And then i looked this value up just in the table.
01:44
Now on the second question, you're dealing with germination of a seed.
01:47
And so there's a 75 % chance of the seed germinating and 145 are going to be looked at of the seeds.
01:55
And so that means n times p, the mean number that would germinate is 108 .75, and that, using that same formula, our standard deviation is 5 .2 -ish.
02:08
Now, the person believes that more than 111 will germinate...