Several psychology students are unprepared for a surprise tr

Several psychology students are unprepared for a surprise true/false test with 17 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?

Solution

a)

The probability of a correct answer here is p = 1/2 or 0.5.

Mean = n p = 17*0.5 = 8.5 [ANSWER]

standard deviation = sqrt(np(1-p)) = sqrt(17*0.5*(1-0.5)) = 2.061552813 [ANSWER]

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b)

The z score for x = 11 is

z = (x-u)/s = (11-8.5)/2.061552813 = 1.212678125

As this is less than 2, the NO, IT IS NOT UNUSUAL. [ANSWER]