00:01
Hi, i'm david and i'm here to have you answered your question.
00:03
Now let me bring up your question here.
00:06
In the question here we are going to discuss about the standard normal distribution.
00:11
In order to answer your question, i need to bring up the z table.
00:14
So let me call me the z table and i will put the table on the right here.
00:24
I will make it bigger.
00:28
Notice that the table i bring here, it has the negative g score with the probability in the left tail.
00:34
Now for the first question 1, we will sketch the i'll sketch the i'll.
00:37
Under the standard normal curve.
00:39
So i will sketch it on the right here and we have the pell curve.
00:46
Now the area between the zero and the three.
00:50
So let's say zero here and the three here and the area we're looking for will be in the yellow shaded region.
00:59
To find this area here we will see the area it will equal to the probability of the z will be between the zero and the three.
01:10
Now because of the symmetry, if we consider the minus 3 on the left, then the area on the left, it will equal to the area on the right.
01:18
And then we can write this down into the probability of the z will be between the minus 3 and the 0.
01:26
And because half of the area is equal to the 0 .5, then we can take the 0 .5, we minus the area on the very left tail here, equal to the probability the z smaller than the minus 3.
01:39
And then we get equal to the subpo.
01:41
Minus and the minus 3 .0, the corresponding probability equal to the subpoena 013.
01:49
And then we get equal to each upon 5 minus 0 .0013 equal to the 0 .987.
01:58
I write to the 4 decimal places.
02:00
And that will be the number one.
02:02
Now for the number two, we will have the area between the minus 2 .16 and the 1 .30.
02:09
So the area in the p, it will be the probability of the z between the minus 2 .16 and the 1 .33.
02:20
So it will try to draw the graph again.
02:22
We will have this will be the pale curve and this will be the 0.
02:29
Suppose this will be the minus 2 .16, this will be the 1 .33.
02:34
Then the area we're looking for will be the one in the yellow.
02:37
Now if you find the one in the yellow, we can tell you, the total area will be a 1 again.
02:43
We minus the eye on the left tail and the left tail it will correspond to the probability the z smaller than the minus 2 .16.
02:51
We minus the eye on the right tail but because of the symmetry we can minus the one on the left tail here and the left tail can be written down as a probability in the z smaller than the minus 1 .33.
03:04
So we can use the table now to get for this one and the minus 2 .1 and 6.
03:13
We get equal to the 0 .0154 for the minus 1 .3 and 3.
03:23
The corresponding probability equal to the 0 .0 918.
03:29
And then we get equal to 1 minus 0 .0154 minus 0 .918, equal to the 0 .8, 28...