00:01
In this exercise, we are asked what proportion of a normal distribution is located between minus 2 and 1 .75.
00:11
Mathematically, we can write this like this.
00:13
What is the probability that z is between minus 2 and plus 1 .75? graphically, it looks like this.
00:30
So let's say this is plus 1 .75, and this is minus 2.
00:37
So this is the standard normal distribution.
00:39
We want to know what proportion of the distribution is between these two values.
00:56
That also is equal to the area that's between these two values, the area underneath the curve between these two values.
01:04
So what we can do to find this is to find first the probability of z being less than 1 .75.
01:13
So this is the area in the distribution below 1 .75.
01:22
And then subtract from that the area below minus 2.
01:30
Once we do that, we are left with the area of interest.
01:39
So mathematically, the strategy is probability that z is less than 1 .75 minus the probability that z is less than minus 2.
01:56
Now we can use a standard normal table to look these up.
01:59
So the first term is the probability that z is less than 1 .75.
02:04
If we go to a standard normal table, look at 1 .7, 1 .75, this this corresponds to an area of .9599.
02:21
And now for the second term, the probability that z is less than minus 2...