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

ID: 3124470 • Letter: S

Question

Several psychology students are unprepared for a surprise true/false test with 12 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 8 correct answers)? Why or why not?

(Round to one decimal place as needed.)

b. Choose the correct answer below.

Yes, because 8 is within the range of usual values.

Yes comma because 8 is greater than the maximum usual value.

No comma because 8 is within the range of usual values.

Yes comma because 8 is below the minimum usual value.

There are 12 questions each has two options as true or false.

Let X be the random variable that the number of correct answers for such students.

X ~ Binomial (n = 12, p = 1/2)

Find the mean and standard deviation for the number of correct answers for such students.

mean () = n*p = 12*(1/2) = 6

variance (var) = n*p*(1-p) = 12*(1/2)*(1 - 1/2) = 3

standard deviation () = sqrt(var) = sqrt(3) = 1.7

Would it be unusual for a student to pass by guessing (which requires getting at least 8 correct answers)? Why or why not?

minimum usual value = - 2* = 6 - 2(1.7) = 2.6

maximum usual value = + 2* = 6 + 2(1.7) = 9.4

This means that anything more than 9.4 questions correct would be unusual, so YES, at least 8 correct would certainly be usual.

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