Question

Use the following information using 20 questions instead of 35

Background:

You are taking a standardized test with 35 questions.
For each question you are given the choice of 5 possible answers A, B, C, D and E.
You answer each question randomly.

What is the probability that you pass the test by answering at least 70 % of the 30 questions correctly? Answer the following questions.

1) Is this a binomial experiment?           Circle one YES                         NO   

Check/Explain the following 4 points in order to determine if it is a binomial experiment/situation.

                1. How many trials do we have?

                2. Are the trials independent?

3. What would be Success?

                4. What is the probability of Success?

Answers I calculated with 35 questions. I need to check using 20 questions to see the difference

1) Yes, this is binomial experiment because:

The trails are independent.

There are finite number of questions.

There are only two possible outcomes: Correct and incorrect answer

Probability of correct answer in each problem is same.

Number of trials = 35

Yes, the trials are independent because probability of correct answer in any question doesn't depend on probability of correct answer in other questions.

Success = Getting a question correct

Probability of success = 1/5 = 0.20

Answer 1

Yes, the given experiment is the binomial experiment.

Now have to use n = 20 questions instead of 35.

p = 0.20 = 1/5

Student pass the test by answering the 70% of the 20 questions correctly.

70% of 20 = 0.70 * 20 = 14

That is student needed atleast 14 question correct to pass the test.

That is student need 14 or more question to answer correctly.

That is,

That is here have to find the probability from 14 to 20, since n = 20

Or we can write out this probability as,

Now using Excel we can direct get P(X < = 13) by using a binomdist function.

= binomdist(13, 20, 0.20, 1) to get 0.999998155

That is the probability that you pass the test by answering at least 70 % of the 20 questions correctly is 0.000002