00:01
We are told that 45 % of customers visiting a shop spends more than 500 of purchases.
00:06
We have a sample of eight of them.
00:07
First thing we want to do is to check if we can use the binomial distribution here.
00:14
So the binomial distribution has four requirements.
00:18
The first is that you need a fixed number of trials.
00:26
Do we have that? well, we're looking at eight people, so yes.
00:30
N is going to be eight.
00:31
The second requirement is they must be independent of each other.
00:37
So we've got a random sample, so it's fair to say they are independent of each other, whether or not one customer spends more than 500 should not affect the others.
00:47
The third requirement is that each trial has two outcomes, which here would be they spend more than 500, or they don't.
00:57
They spend 500 or less.
00:59
So we've got two outcomes for each person.
01:01
You also need a consistent probability p of success on each trial, which here means the probability they spend more than 500.
01:13
So basically, this means that we don't change things halfway through.
01:16
We don't start a sale halfway through the experiments and therefore change how much people are willing to spend.
01:24
Here, p is going to be the 45 % chance, and we're putting that in decimal form.
01:29
So those are the four requirements.
01:33
Part b.
01:36
Now x is the binomial variable, the number in the sample that meet the criteria.
01:41
We want the probability x is exactly 3.
01:45
So i'm going to use excel here with the function binom .dd...