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Mark is sitting a statistics test, which consists of 10 questions where each question has four possibilities (A, B, C & D) but only one is correct. After the test, Mark told you he didn’t study for the test at all and guessed all answers.
(a) If Mark 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 4 decimal points in your answers. (Use Excel to calculate the probabilities.)
(b) Using the formula: E(X) = XP(X), find out the number of incorrect answers Mark would expect to get. (You can use Excel to do the calculation. Just copy the Excel output onto your Word document.)
(c) What does expectation mean in statistics? Explain your answer in the context of the A to D Test.
(d) What is the probability that Mark gets 8 or more correct answers for this test?
(e) When the result was released, Mark got 3 out of 10. Would you be surprised? Do you think Mark lied to you? Explain your answer