5 a student takes a multiple choice test that has 10...

A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Model a discrete probability distribution for the number of correct answers on this test as a binomial probability distribution. a) Find P(3). b) Find P(More than 2). c) What is the mean of the expected number of correct answers from this probability distribution? d) What is the standard deviation from the mean of the number of correct answers from this probability distribution? e) To pass the test, the student must answer 7 or more questions correctly. Would it be unusual for the student to pass? Explain.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Let me bring up your question here.

00:06 Now in this question we will review about the binomial distribution.

00:10 We continue that if we have x followed by the binomial n p and p and then the probability x equal to k, it will equal to the n choose k, p power k times 1 minus p power n minus k.

00:27 Also mean on the e of the x is equal to n times p and the variance on the x equal to the n times p times 1 minus b.

00:38 Now we want to model the x as the number of the correct answer and then we will have x it will follow by the binomial.

00:48 With the end we have here will be 10 questions and the probability of success will be the correct one because it is a multiple choice and each question has four choices.

01:00 So the b equal to 104 and equal to 0 .25 and now in the part a we want to find the probability x equal to 3 so if we apply the formula here we should get now 10 to 3 0 .25 0 .25 power 3 1 minus 0 .5 25 will be 0 .75 power 7 if we do the calculation 0 .75 power 7, you get equal to the 0 .25 to 8.

01:47 And that's going to be the answer for the a.

01:50 Now for the b, what is the probability that more than 2? so x greater than 2.

01:58 Now by the complement, this one equals to 1 minus probability x smaller equal to 1.

02:03 So it is equal to 1 minus probability x equal to 0, minus probability x equal to 1.

02:11 So we have 1 minus here 10, choose 3 times 0 .25, this is 1 0 .20 first, 6.

02:20 And then we have the 0 .75 power 10, minus 10 choose 1, 0 .25 power 1, 0 .75 power 9.

02:32 If we do the calculation, we will have here 0 .25 number child equal to 10...

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