In: Statistics and Probability
A true/false test has 100 questions. A passing grade is 64% or more correct answers. a. What is the probability that a person will guess correctly on one true/false question? b. What is the probability that a person will guess incorrectly on one question? c. Find the approximate probability that a person who is just guessing will pass the test. d. If a similar test were given with multipl-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?
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Answer:
c)
to pass we need the proportion of correct to be above 0.64
p =0.5
q = 0.5
z = 0.64 - 0.5/0.070711
= 1.9799
We need to find P(Z<1.9799) for passing
From the z table we find that the probability is 0.023857 ~ 2.34%
d)
In case of 4 options, the probability of passing reduced to 1/4 = 0.25 and there will be lower probability for p to exceed 64% and hence lower probability of passing