00:01
In this problem, we have a binomial distribution with a fixed number of trials of nine and a probability of 0 .905.
00:09
So for a, it wants to know what is the probability of at least eight of them, so eight or nine, being admitted.
00:21
So what we could do here is we can do one minus and use the binomial cdf function in our calculator.
00:32
And it will subtract 7654321 and 0 from the total distribution, which we know is 100%.
00:41
And that will give us the two options of 8 or 9.
00:47
So 0 .905.
00:52
And my calculator gives me a lower and upper bound, so i just did lower of 8, upper of 9 .791956.
00:59
So part b, what is the probability that exactly six graduated? so this would be binomial pdf, n of 9, p of 0 .905, and an x of 6.
01:19
So 9 .95 and 6, and that is a 0 .039 .68.
01:31
About a 3 .9 % chance of that happening.
01:34
So part c, would it be unusual? yes, because the probability of getting six, which was the 0 .039, is less than 5%.
01:45
That's kind of our cutoff for our unusual or not unusual events.
01:50
D, find the probability that at most six, so less than or equal to six, that would be binomial cdf, n of 9, p of 0 .905, and x of 6.
02:05
So same thing we did before, but it's binomial cdf.
02:15
And that probability is going to be 0 .0465...