Question

Multiple Choice Test

Chris is sitting a multiple choice test in statistics. The test consists of 9 items and each item has 5 options. After the test, Chris told you he didn’t study for the test at all and guessed all answers.

If Chris guessed each and every item in the test, describe the probability distribution for the number of correct guesses. Present the probability distribution in the form of a table using 6 decimal points in your answers. (Use BINOM.DIST function to calculate the probabilities.)

In lecture, we showed you a simple formula for finding out the expected value of a binomial distribution: E(X) = n´p - Formula 1. Since binomial distribution is a discrete probability distribution, we can also use the formula: E(X) = åX*P(X) - Formula 2, to find out its expected value. Use Formula 2 to find out the number of correct answers you would expect Chris to get.

Note: You can use Excel to do the calculation and copy the Excel output onto your Word document. You are also advised to check your final answer using Formula 1.

What does expectation mean in statistics? Explain your answer in the context of this Multiple Choice Test.

What is the probability that Chris gets 5 or more correct answers in this test, If Chris randomly picks answers to all 9 items?

When the result was released, Chris got 5 out of 9. Based on this mark if you determined that Chris lied to you, could you be wrong? If you were wrong, what type of error have you committed? What is the probability that you were wrong?

If Chris did get 5 out of 9 (and passed!), would you believe that Chris guessed every item in the test?

Note: You won’t get any mark for answering this question, but you are encouraged to attempt this question, and discuss it with your classmates.

(0 mark)

Answer 1

the test contains a total of 9 questions. So n=9

there are 5 options to every single question, and one is correct. So the probability to make the right guess is for every single question.

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring.

Here the expected value of the questions that Chris can get correct is

the probability that Chris gets 5 or more correct answers in this test=

Based on this probability that Chris made the right guesses is 1.65%, which is pretty low.

If you were wrong, you have committed a type I error. Probability that you were wrong is 0.016515