Several psychology students are unprepared for a surprise true/false test with 9

Question

Several psychology students are unprepared for a surprise true/false test with 9 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 7 correct answers)? Why or why not? a. mu = sigma = (Round to one decimal place as needed.) b. Choose the correct answer below. A. Yes, because 7 is below the minimum usual value. B. Yes, because 7 is within the range of usual values. C. No. because 7 is within the range of usual values. D. Yes. because 7 is greater than the maximum usual value.

Explanation / Answer

a) p =1/2 ,q = 1 -1/2 = 1/2 , n = 9

X = np

E(X) = np = 9*1/2 = 4.5

sd = sqrt(npq) = sqrt(9*0.5*0.5) = 1.5

b) P(X >= 7 )

=P(X> 6.5) {continuity correction }

=P(Z > (6.5 - 4.5)/1.5)

=P(Z > 2/1.5)

=P(Z> 1.333)

=0.0912

Since Probability > 0.05

No ,this is not unusual

option C) is correct

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