At a local community college, 60% of students who enter the...

At a local community college, 60% of students who enter the college as freshmen go on to graduate. Eight freshmen are randomly selected. a. What is the probability that none of them graduates from the local community college? (Round your answer to 4 decimal places.) Probability b. What is the probability that at most seven will graduate from the local community college? (Round your answer to 4 decimal places.) Probability c. What is the expected number that will graduate? (Round your answer to 2 decimal places.) Expected number

Transcript

00:01 Hey there, welcome to numerade.

00:04 We are given here that 60 % of students who enter college goes on to graduate.

00:11 So therefore, we have the 60 % represented as a decimal, which is 0 .60, and we have our sample size here equaling 8.

00:28 So therefore, this here follows a binomial distribution, since we're given in a paper.

00:34 Trials, it fixed probability and two outcomes.

00:39 So we're going to start with the binomial coefficient, n choose x, multiplied by p, raised to the x, which is multiplied by q raised to the n minus x.

00:53 So knowing this here, we can start with part a in which we're looking at, that zero graduates from the local community college.

01:05 So the probability of zero.

01:07 So we can directly plug in this value into our equation in which we basically have 8 choose 0, multiplied by our probability, and then raise to the 0 times 1 minus the probability, which is 0 .4, raised to the 8 minus 0, which is 8.

01:34 All right so therefore this gives us a probability of zero that equals around 0 .000 and then we're going to round the last decimal to a 7 all right try part b part b that at most 7 will graduate the probability that x is less than or equal to 7 is basically at most so for this we are going to start with the probability of seven and go downwards.

02:17 So we can add going downwards.

02:20 And we're going to keep on going downwards here all the way down to the probability of zero...

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