00:01
Hello.
00:04
So this is the given information.
00:06
So let's look at a.
00:09
We want to find the probability that the sample proportion is between 0 .172 and 0 .178.
00:23
0 .172 and 0 .178.
00:37
So it's going to be 0 .172 minus proportion.
00:45
This is the population proportion, that's 0 .1 divided by the standard error, which is given by the square rule of the population proportion, 0 .1 minus, excuse me, 0 .1 into 1 minus 0 .1, divided by the sample size 100.
01:11
So here we are doing p hat minus p divided by p into 1 minus p divided by n.
01:20
We have square root of that.
01:25
Then on the right we have 0 .178 minus 0 .1 divided by square root of 0 .1 into 1 minus 0 .1 divided by 100.
01:50
So let's see what we're going to get.
01:52
So you have 0 .172 minus 0 .1 divided by square root of 0 .1 of 0 .1 times 0 .1 .1.
02:04
Divided by 100 this is going to be 2 .4 this is z let's see what we get here this is going to be 2 .6 so now we can rewrite this as the probability of z less than 2 .6 minus probability of z less than 2 .4 let's keep in mind that because of our sample size is large or greater than 30, so we are using the z distribution.
02:51
So now we go to the z table, look for 2 .6, and the corresponding probability is 0 .99534.
03:07
99534...