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A multiple-choice exam has four possible answers for each question. For each correct answer, you are awarded 5 points. For each incorrect answer, 2 points are subtracted from your score. For answers left blank, no points are added or subtracted. (a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain. (b) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain.

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SumantLv10
4 Apr 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

A quiz has 25 multiple choice questions. Each question has 5 possible answers, one of which is correct. A correct answer is worth 4 points, but a point is taken off for each incorrect answer. A student answers all the questions by guessing at random. The score will be like the sum of (a.)____ draws from the box (b.)______. Fill in the first blank with a number and the second with a box of tickets. Explain your answers.

A deck of n cards numbered 1 through n is thoroughly shuffled so that all possible n! orderings can be assumed to be equally likely. Suppose you are to make n guesses sequentially, where the ith one is a guess of the card in position i. Let N denote ht number of correct guesses. (a) If you are not given any information about your earlier guesses show that, for any strategy, E[N]=1. (b) Suppose that after each guess you are shown the card that was in the positionĀ  in question. What do you think is the best strategy? Show that, under this strategy.

Ā 

(c) Suppose that you are told after each guess whether you are right or or wrong. In this case, it can be shown that the strategy which maximizesĀ  E[N] is one that keeps on guessing the same card until you are told you are correct and then changes to a new card. For this strategy, show thatĀ 

Ā 

Hint: For all parts, express N as the sum of indicator Hint: For all parts, express N as the sum of the indicator.

Ā 

Rules of dice game:

ā€¢ All players start with 10 points

ā€¢ A dice is rolled, and if the number on the dice is 1, 2, 3, 4 or 5, this number is added to each player's score. If the number is 6, the score off all players is reduced to zero

ā€¢ Before the dice is rolled each player is given the choice of continuing or taking their current score as their final score.

ā€¢ This process is repeated until a 6 is rolled and the game ends. All players still playing at this point receive zero as their final score.

Suppose that you choose to play the first dice roll.

(i) Compute the expected value and standard deviation of your score after the first dice roll.

(ii) On average, do you do worse or better than someone who choose not to play and take 10 as their final score?

Now suppose that a 6 was not rolled and you chooses to continue playing

(iii) On average, what score would you have before the dice is rolled?

(iv) Compute the expected value for your score after the second dice roll.

(v) On average, do you do worse or better than someone who choose to stop playing after 1 dice roll?

(vi) Is there an optimal number of dice rolls you should continue playing for? Explain your reasoning.

(vii) If the rules are changed such that when the number is 2, 3, 4, 5 or 6, this number is added to your score. While if the number is 1, your score is reduced to zero. Discuss how this affects the optimal number of dice rolls you should continue playing for.

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