Math  /  Data & Statistics

QuestionA multiple-choice exam contains questions that each have 4 answer choices. One point is awarded for each correct answer, and 0.25 points are deducted for each incorrect answer. If an answer is left blank, then points are not awarded or deducted. Round the expected value to the nearest hundreth. a. What is the expected value if a student guesses on a question? \square b. Is it advantageous to guess if an answer is unknown? ? V c. What is the expected value if 0.5 points are deducted for each incorrect answer? \square

Studdy Solution
Calculate the expected value for a guessed answer with a 0.5 point deduction:
The expected value E E is calculated as follows:
E=(14×1)+(34×(0.5)) E = \left(\frac{1}{4} \times 1\right) + \left(\frac{3}{4} \times (-0.5)\right)
E=1434×0.5 E = \frac{1}{4} - \frac{3}{4} \times 0.5
E=0.250.375 E = 0.25 - 0.375
E=0.125 E = -0.125
The expected values are:
a. 0.06 \boxed{0.06}
b. It is advantageous to guess if an answer is unknown.
c. 0.13 \boxed{-0.13}

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