00:02
Hello, so this is a normal distribution question.
00:06
These are the parameters given.
00:09
So let's look at how to find a.
00:12
It's going to be the probability.
00:16
And the sample average is more than that.
00:19
So we got a sample average is more than 2 .35.
00:30
For a normal distribution, it's going to be x bar minus a minute over standard deviation, divided by the square root of n greater than 2 .35 minus 2 .65 divided by 0 .85 divided by square root of 25, which is just 5.
00:57
Right? so you have 2 .35 minus 2 .65 divided by 0 .85, divided by 0 .85, divided by 5.
01:18
This right here is the z that's going to be greater than negative 1 .76.
01:35
This is the same as 1 minus the probability of z less than negative 1 .76.
01:44
So i'm going to go to my z table and look for negative 1 .76 and get the corresponding probability.
01:54
So for z equals that.
01:58
The probability when z is negative 1 .776 from the z table is 0 .3920.
02:11
So that's 0 .03920.
02:24
And so our required probability is 1 minus that.
02:34
So we're going at 0 .9608.
02:40
B is at most 3.
02:44
So that's probability of x bar less than equal it 3.
02:50
That's at most.
02:53
So we're going to have the same thing.
02:58
Formula over standard division divided by that less than equal to 3 minus 2 .65.
03:13
Over 0 .8, divided by square root of 25.
03:24
Again, if you just have z, less than equal to 3 minus 2 .6.
03:35
5 divided by 0 .8.
03:43
That's a second.
03:44
0 .8 divided by 5.
03:52
That is 2 .1875.
03:59
So to refraise the table, we're going to round this up to 2 .19.
04:08
For 2 .19, for 2 .19, the probability 0 .98, 0 .98 .5, 4.
04:34
Okay, let's look at c.
04:39
C is between two numbers.
04:41
So we got probability of 2 .35 where is that? x bar, let's not try.
05:00
So that is just...
05:02
So what did we get for 2 .35? so we got that.
05:10
So i'm just going to say probability of negative 1 .0 z.
05:22
What did you get for 3? today we got this, right? that's 2 .1875.
05:32
2 .1875.
05:36
So we can rearrange this as probability of z less than 2 .1875 minus the probability of z less than negative 1 .76.
05:51
We have these numbers already.
05:53
For this one, 0 .574...