Question
In: Statistics and Probability
Several psychology students are unprepared for a surprise true/false test with 13 questions, and all of...
Several psychology students are unprepared for a surprise true/false test with 13 questions, and all of their answers are guesses.
a. Find the mean and standard deviation for the number of correct answers for such students.
b. Would it be unusual for a student to pass by guessing (which requires getting at least 11 correct answers)? Why or why not?
Solutions
Expert Solution
Given there is a surprise true/false test with 13 questions.
Therefore, the probability of correctly guessing the answer is p=0.5
Let "X' be the answers correcly guess by a student.
Therefore, 
The pmf od X is:
for x=0,1,2,...,n
a) The mean of the binomial distribution is:
The standard deviation is:
b) The probability that the student getting at least 11 correct answers is given by:
Since the probability is less than 0.05, we say that it is unusual for a student to pass by guessing.
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