[MUSIC] Let's get back to the example of cereals. We are looking for mu. What we know, We know that based on the sample that we have, the average weight of 30 packs of cereals would be 30, it's 301.5 grams. We have to add one piece of information here. The piece of information, as you could already imagine from before, was that we were missing this bit. Which is the actual variants of the population, in terms of gram. So let's assume it's just 1 gram, we also were told that we're talking about 95% confidence. So let's try to plug back in the values. So we said that the mu, with 95% confidence, will be 301.5 grams plus minus 1.96 1 over square root of 30. In other words, we can say that, with 95% confidence, we can say that mu will be in this region. So let's try to calculate the upper and the lower bound of this confidence interval. So the upper bound, that's called the upper bound of mu, will be 301.5 + 1.96 1 over 300, which will be equal to 301.86. The lower bound of this mu will be 301.5- 1.96 1 over 30, which will be 301.14. So if you want to picture this, if this is our confidence interval, the x upper bar will be always in the middle, 301.5 grams. This is our mean, the sample mean. The lower bound will be 301.4 grams and the upper bound is 301.86 grams. So what we can say that with 95% confidence, we know that our mean of all the population, of all the cereal boxes that is produced by this manufacturer, will be definitely above this 300 grams that are advertised on the box. Now, it's very important to produce this kind of information because from consumer perspective, it will be important that the consumers will have the correct information on the boxes. So if, with 95% confidence, we can say that the cereal boxes, all the cereal boxes, produced by this manufacturer are above 300 grams, then I would be suspecting that consumers will not complain. However, if we find that with 95% confidence, this is below 300 grams, then the producer has a problem that it may face legal suits against himself or herself in those situations. So the statistic information that is encoded within the confidence interval will be quite important to this kind of producer. [MUSIC]