00:01
For this problem, we have to draw a graph for the standard normal distribution and label the horizontal axis from negative 3 to 0 and then to 3.
00:11
So a standard normal distribution has a mean of 0 and a standard deviation of 1.
00:17
So graphically, this is how it looks like with a bell shaped and a horizontal axis.
00:27
Move on to the questions.
00:29
We have to find the probability that z is less than or equal to 1 .1.
00:37
We are to use the table of probabilities here, also known as the z table.
00:48
The one we are to note is that, say you have a standard normal with a certain z value.
01:00
The probabilities under the z table correspond to the area to the left of z.
01:06
That is this region here.
01:10
So for this problem, where z equals 1 .5, you're interested in the region to the left of z.
01:18
The probability is simply the area under the graph, which is equal to 1 .5.
01:22
The value we obtained from the z table.
01:29
So now this is equal to the normal of 1 .5.
01:35
So from the z table, we locate 1 .5 from the z column that is here.
01:44
And then under the column .00, so this is where the two intersect.
01:53
And the value there is 0 .9332...