00:01
We consider a binomial experiment where the probability of success on each trial, which is denoted p, is 0 .35, and we are asked to find the probability that in a sample of size 50, the proportion of successes exceeds 0 .2.
00:21
So the random variable x is the number of successes in a sample of 50.
00:27
And it's a binomial experiment, so x follows a binomial distribution.
00:31
So its parameters are n equals 50 trials, p equals 0 .35 probability of success on each trial.
00:48
One way to solve this is to find out how many successes is 0 .2 of the sample size of 50.
00:56
So if we multiply 50 times 0 .2, this is 10.
01:07
And so we want to find the probability that the proportion of the sample that our successes exceeds 0 .2, therefore we want to find the probability of more than 10 successes.
01:22
Now to solve this, we're going to use software.
01:24
We first have to re -express it in terms of a cumulative probability.
01:28
This is equal to 1 minus probability that the number of successes is at most 10.
01:36
And now that we have to express this way, we can solve this using software such as excel.
01:41
Let's solve the whole expression in one step...