Suppose a multiple choice test contains 30 questions. If each question has 5 answer choices only one of which is correct, what is the expected number of questions to be answered correctly by guessing?  The SAT used to penalize wrong answers by subtracting 1/4 a point from each incorrect answer. If each question on the SAT has 5 answer choices only one of which is correct, what is the expected number of points awarded by guessing on 30 questions?

Question
Asked Oct 9, 2019

Suppose a multiple choice test contains 30 questions. If each question has 5 answer choices only one of which is correct, what is the expected number of questions to be answered correctly by guessing?

 
 

The SAT used to penalize wrong answers by subtracting 1/4 a point from each incorrect answer. If each question on the SAT has 5 answer choices only one of which is correct, what is the expected number of points awarded by guessing on 30 questions?

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Expert Answer

Step 1

An experiment with two possible outcomes follows the binomial distribution.

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

 

n
*
p*q*
x= 0,1..7;0 <p<1;q 1-p
P(x)
|0
otherwise.
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n * p*q* x= 0,1..7;0 <p<1;q 1-p P(x) |0 otherwise.

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Step 2

Let X is the number of correct answers, which follows the binomial distribution with parameters n, p.

A multiple choice test contains 30 questions and each question has 5 choices out o...

n=32
1
p
5
Mean np
32 (0.2)
6
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n=32 1 p 5 Mean np 32 (0.2) 6

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