A university found that 16% of its students withdraw without...

A university found that 16% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. If required, round your answer to four decimal places. (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.

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00:01 Hey there, welcome to numerate.

00:04 So we're looking at the percentage of students that withdraw their intro stats class without actually completing it.

00:12 This percentage is 16%.

00:15 And we're given a sample size of 20 students here.

00:19 So again, let's write down percentage, which will reflect our probability, 0 .16, and a sample size of 20 students in the course.

00:31 So for part a over here, we're asked to find the probability that x is two or fewer without drawing, so less than or equal to two.

00:43 And what we have basically here is a binomial setup.

00:47 The binomial equation is the probability of x equals combinations n x multiplied by the probability raised to the x, multiplied by n minus x.

01:04 So for this probability here, we have the probability the x is less than or equal to two.

01:14 So two or fewer, so it will be the probability of two plus the probability of one and plus the probability of zero.

01:26 So we're going to plug each of these values, x values, into our equation here.

01:34 Okay.

01:35 And we basically get our probability once we do that to our fewer.

01:41 So we get a probability of 0 .3 -580.

01:49 All right.

01:56 So this is four decimal places...

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