00:01
In this question, we are given the probability.
00:02
So the probability of someone just having the allergy, which is 8%.
00:06
Let's denote by p, which is 8%, which is 0 .08 here, and the sample size here, which is given as 10.
00:13
So we know the sample size, we know the probability, so we have to use a binomial distribution.
00:18
Let me define the random variable x for the binomial distribution, the 10 and the 0 .08.
00:23
So x denotes the number of people who just have the allergy.
00:31
And so what we have to calculate here, so part a, the probability of random variable x, which is 3.
00:38
For the binomial distribution, the random variable should be discrete.
00:40
So if x is less than 3, so that means the x should be less than or equal to 2.
00:45
So the open form of this one would be x is equal to 0 plus x is equal to 1 and plus x is equal to 2.
00:52
In order to get the probability, let's remember the formula.
00:56
When x is equal to r, this is combination nr times p to the power r, and 1 minus p to the power n minus r.
01:04
So you can just apply for each of them separately and then add them up.
01:08
So instead of this, you can also use the graphing display calculator application binomcdf.
01:14
So the n value here is 10 and the probability is 0 .08, and the x value here included, which is 2.
01:21
Press second, variance, the binomcdf.
01:24
I'm gonna find this value on the bottom of the page.
01:26
So this is 10, 0 .08, and 2.
01:31
So the probability would be with how many three decimal places i can just write this is 0 .960.
01:38
And the b here, which is the x is less than or equal to 3.
01:41
In this case, the 3 is included.
01:43
So again, i'm going to use the binomcdf.
01:46
So this is 10, 0 .08, and the 3 here...