Several psychology students are unprepared for a surprise true/false test with 1

Question

Several psychology students are unprepared for a surprise true/false test with 15 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 10 correct answers)? Why or why not? mu = sigma = (Round to one decimal place as needed.) b. Choose the correct answer below. Yes, because 10 is below the minimum usual value Yes, because 10 is greater than the maximum usual value. Yes, because 10 is within the range of usual values. No, because 10 is within the range of usual values Click to select your answer(s).

Explanation / Answer

Part-a

Sample size n=15

Probability of correct answer p=1/2=0.5 ( as there are only two choice true/false)

Mean =np=15*0.5=7.5

Standard deviation =sqrt(np(1-p))=sqrt(15*0.5*(1-0.5))=1.9

Part-b

X follows binomial with n=15 and p=0.5

So, P(X>=10)=1-P(X<=9)=0.1509 using excel function =1-BINOMDIST(9,15,0.5,TRUE)

So , it is not unusual to pass by guessing as this probabaility is >0.05

Option D

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