A true/false test has 70 questions. A passing grade is 59% or more correct answe

Question

A true/false test has 70 questions. A passing grade is 59% or more correct answers. What is the probability that a person will guess correctly on one true/false question? What is the probability that a person will guess incorrectly on one question? Find the approximate probability that a person who is just guessing will pass the test. If a similar test were given with multiple-choice questions with four choices for each question, would the approximate probability of passing the test by guessing be higher or lower than the approximate probability of passing the true/false test? Why?

Explanation / Answer

A)

p = 0.5 [ANSWER]

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b)

q = 1 - p = 1 - 0.5 = 0.5 [ANSWER]

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c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.59      
u = mean = p =    0.5      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.05976143      
          
Thus,          
          
z = (x - u) / s =    1.505988048      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.505988048   ) =    0.066035121 [ANSWER]

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d)

It would be LOWER, as we only expect him to answer 1/4 = 0.25 of the problems, on the average. Hence, 0.59 is farther from that.

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