00:01
So in this question we have that a recent study has shown that 28 % of like 18 and 34 years old check the facebook or instagram feeds before getting out of bed in the morning.
00:13
So i'm going to say that in this research, the proportion of this specific age group that checks their social media before getting out of bed is 0 .28.
00:27
Now consider that we have a sample of 150 of the same group of people.
00:34
We want to check what is the first in item a.
00:38
What is the probability that the number of students here that check in this sample, they check their social media before getting out of bed is actually study.
00:51
So i'm going to say the x here is the number of people that does that kind of things.
00:57
So the number of people that checks their social media and before getting out of bed.
01:08
But just the number.
01:10
So x here represents the number of people in this sample collected here, 150.
01:15
So in item a, we should say or find what is the probability that we are going to find 30 out of this 150 that does this.
01:25
So basically here, the questions say that we should use the approximation to the number.
01:29
Normal distribution.
01:31
So to use the approximation to the normal distribution, we have first to compute what is the mean here that we are going to use.
01:39
So the mean, in this case, is given by n times p, so 150 times 0 .28, which is 42.
01:51
And the standard deviation that i'm going to call sigma is the square root of n times p, 1 minus p.
02:00
And this is also the multiplication.
02:03
So basically he will be 150 times 0 .28 times 1 minus 0 .28.
02:11
So if you compute this, you're going to get 549 .91.
02:18
So now, to compute this probability using this approximation, we should use the correction factor.
02:25
So basically here, and you can find online, if you have greater and 8 ,000, equal here this means that i should transform this to be in this case just greater and i should subtract 0 .5 because of the correction to the normal distribution.
02:43
So here we have x is greater than in this case 29 .5.
02:49
And using this mean and this standard deviation we are going to compute this probability here now using a normal distribution with this mean and this standard so the idea here is that the probability of x being graded in 29 .5 using the z score approach is now going to change z because the z score approach uses the standard norm distribution to compute probabilities.
03:19
And the idea here is that we should subtract the mean that we have and the standard deviation that we computed before.
03:27
So now if you compute this, you're going to get z is greater.
03:32
Then minus 2 .2731.
03:36
And using the z table, you're going to get that this probability is equal to this here.
03:43
Now for item b, we should compute what is the probability than no more, or in this case, less or equal than 50.
03:51
People you're going to find that they check their social media before getting out of that in the morning...