00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:09
In this question we're going to review about the normal distribution.
00:13
Let me remind you that even the x followed by the normal with the mean and standard deviation, then we can take the x minus the mean of a standard deviation to get the standard normal.
00:25
Here in the question a, we're given the x followed by the normal with the mean equal to 100, standard normal.
00:33
Division equal to 10.
00:35
Once you find the probability that x to the left of the x, so smaller than equal to the small x, such that doesn't equal to the 96 .85 percent or i will equal to 096 0 .9685.
00:59
And here we need to convert the x here into the zi by using this formula here.
01:07
And then it will equal to the proverb p to the z small equal to x we have to minus the mean of a standard division it will equal to the z -point nine six eighty five now let me bring up the z table and also you have to use the z table here let me put the table on the right here now we will not be able to see the value of this one but we can find the one minus z upon nine six eighty five then we get equal to the 0 .0 315.
01:49
It will look up the table.
01:51
We have 0 .0 .0315.
01:57
We have this one, 3 .0 314, very close to that.
02:01
It corresponds to the value minus 1 .86.
02:05
So therefore, it will equal to proper between the z smaller than equal to the minus 1 .86.
02:15
And then we want to have is equal to the 0 .9 .685, therefore the 0 .9 .685 must equal to the proper p.
02:27
Z smaller equal to the quantity of that because of the symmetry...