00:01
Hello.
00:03
So this is the given information and we want to find the probability of x equals 34 or x equals 35.
00:24
This is equal to probability of x equals 34 plus probability of x equals 35 okay now this is a normal distribution.
00:39
Normal distribution is a continuous distribution and so this is going to be a problem we don't have equal to sides uh in normal distribution it has to be an inequality so what this means is that this is going to be the same as the probability so we can rewrite for the 34 we can do 33 .5 less than x less than 34 .5 plus probability.
01:15
So this is going to be 34 .5 x less than 35 .5.
01:24
So you can see that the average values of this is always going to be.
01:27
So this for this is going to be 34.
01:29
The other one is going to be still 35.
01:31
So now we can use the normal distribution to solve this now.
01:37
So what i'm going to do is to first solve for probability of 303 .5 less than x less than so this for normal distribution is going to be 33 .5 minus 30 divided by standard division 3 .9 we have a formula in the middle on the right we're going to have 34 .5 minus 30 divided by standard division so now let's see so we have 33 .5 minus 30.
02:29
So we have 33 .5 minus 30 divided by 3 .9.
02:37
So we're going to have 4 here.
02:39
We're going to get 0 .90.
02:44
This is z.
02:49
Then this side is 34 .5.
02:58
Here we're going to have 1 .15.
03:07
So this is going to be probability of z less than 1 .15 minus probability of z less than 0 .95 minus probability of z at this point, we will need the z table to get its probabilities.
03:29
So let's first look at the probability when z is 1 .15.
03:37
That's 0 .87 -493.
03:41
0 .87 -493 minus 4 .9.
03:47
We have 0 .9 .594.
03:53
So we have 0 .87, 493 minus 0 .81, 594.
04:08
Our probability is going to be 0 .0599.
04:19
So that is for this one...