00:01
So in this question, basically look at the heights of mayor students, right? so the question says that the height of the students follows a normal distribution, right? so suppose x is the height of a mayor student, then it follows a normal distribution with a me of 70 inches and a standard duration of 2 .8 inches.
00:20
So you ask three questions.
00:22
The first one says, if you choose a student at random, what is probability that he is between 69 and 71 inches tall, right? so you look at the distribution of x at a forest normal distribution like this, right? 70, and you look at the area, look at the interval, i mean, the, the, the, the, the heights between 69 and 701, right? so basically look at the percentage that's given by the area in between these two areas, right? so, and if you call this alpha, then this area of versus 1 minus 2 alpha, right? so what we need to do is just to find the value of alpha, right? so the value of all of it can be obtained actually from the z score.
01:04
So the z squared alpha is simply given by 17 minus 69 over the standard deviation 2 .8, right? so that is actually given by 1 divided by 2 .8.
01:15
And of course, that gives you 0 .36, right? now you look up the z table, you find out of a course, 35 .94.
01:25
35 .94%.
01:28
And they, of course, the probability is just a 1 minus, you know, about 36%, right? so it's actually 1 minus 35 .94%, right? and i found this to be actually, so 2 out of it's actually about 28 .12%.
01:59
So that's a probability.
02:00
And the b question is, so first you measure 25 students, what's the sample distribution with the average height? well, the average height is opposed to x obviously also follows a normal distribution, right? because the individual student distribution is normal...