00:01
So in this question, x is a binomial variable with n equals 380 and p equals 0 .78.
00:11
Now this is a much larger n than we would be able to do by hand.
00:15
So in order to find probabilities, what i'm going to do is i'm going to use the programming language r, in which we can write that the probability that x is less than or equal to some quantile x can be given by p binomial x, 380 and 0 .78.
00:36
So we'll just put that into r.
00:39
So first of all, we want the probability that x is less than or equal to 300.
00:44
So i'm going to put in p binomial with quantile 300, size 380, and probability 0 .78.
01:00
And this gives me a probability of 0 .691 to four decimal places.
01:08
Now part b, we want the probability that x is greater than 320.
01:12
Well, that's 1 minus the probability that x is less than or equal to 320.
01:18
So what i'm going to do is i'm going to write 1 minus p binomial, but now with a quantile of 320, but all the rest of it the same, and this gives me 0 .001 -0 to four decimal places.
01:40
Part c, what's the probability that x is between 305 and 325? well, that's the probability that x is less than or equal to 325 minus the probability that x is less than or equal to 304.
01:58
Because remember, i've got to include 305.
02:02
So again, i'm going to use p binomial to work this out, but i'm going to subtract two p binomials from each other.
02:10
So i'm going to have p binomial of 3 .5...