00:01
Hey there, welcome to numerate.
00:03
So we are looking at the proportion who orders coffee with their dinner, and we give the sample size here.
00:11
So we know this is a normal distribution.
00:14
Let's write down our proportion here.
00:19
So our p proportion is 0 .9, and we have a sample size of 144.
00:34
So with this here, we're trying to find the problem.
00:37
The probability where the proportion is between 0 .83 and 0 .855.
00:52
So in order to find this proportion here, we need to split this probability into two parts, where p is less than 0 .855, and the proportion where p is less than 0 .855, and the proportion where p is less than 0 .8 .3.
01:22
All right.
01:24
So let's do 0 .855 first.
01:27
We're going to set up the score equation.
01:29
So we take our 0 .8 .55 minus it to our population proportion of 0 .9 divided by the square root of our population proportion 0 .9.
01:49
Or if we can just do 0 .9 times 1 minus 0 .9 is 0 .1.
01:55
Divided by our sample size of 144.
01:58
Let's see what we get for our z score here.
02:02
So we have 0 .855 minus 0 .9 divided by the square root of .9 times .1.
02:14
.9 times .1 divided by 144.
02:21
This gives us a z score of negative 1 .8.
02:28
And we can now use the z score to find probability by using a table or a calculator.
02:33
So we have negative 1 .a which works out perfectly and gives us a probability of around 0 .0359.
02:45
All right.
02:49
0 .0359.
02:52
So let's save this probability here for later.
03:00
0 .0359.
03:02
Now we're going to work on this probability here...