00:01
Hey there, welcome to numerate.
00:02
We have a show called the voice right here.
00:05
Look at the number of viewers with the mean of 29 million and standard deviation 5 million.
00:11
So if this sample of this distribution is normal, what is the probability that the next week shows will have more than 30 .5 million viewers? so let's label this as part a.
00:26
So we're trying to find a probability, right? so we're going to use a z -score equation.
00:29
So we, let's see, we define our, let's define our variables here first.
00:39
So what we have is mu.
00:41
Mew is the population mean, which is given as 29 million, so 29.
00:47
And we have the sigma, which is basically a population standard deviation, which is five.
00:53
Right.
00:54
So just keep that in mind.
00:55
So the one that we were dealing with is have more than 30 .5 million.
01:01
So it would be the probability.
01:07
The x would be greater than 30 .5.
01:16
That's our probability we're trying to find here.
01:18
So let's put in 30 .5 into our equation, minus our population mean, 29 divided by 5.
01:30
All right, so let's see what we will get here with our score as 30 .5 and 29 is our mean, and then 5 as our standard deviation.
01:41
So let's check out arrows here, 95, 5, and 30 .5.
01:47
And this will give us a z score.
01:49
This is not a probability, but our z score of around 0 .30, which corresponds to a z score of, let's see, of around 0 .3421.
02:04
Sorry, 0 .3821.
02:13
Okay, yep, let's just keep it as four decimal places.
02:16
So that is our probability.
02:18
0 .3821.
02:20
Okay, awesome.
02:22
So let's do the next part.
02:23
I'll label it as part b.
02:27
Part b is 10 % of the shows attracted more than what number of viewers...