Question 7: The final exam in a math class has 50 multiple-choice questions, eac

Question

Question 7: The final exam in a math class has 50 multiple-choice questions, each with four options and exactly one correct answer. A student needs 60% or better on their final in order to receive a passing grade in the class. Their alarm clock broke, and they arrive at the exam with just enough time to guess at each of the questions. Find the mean of the number of correct answers.

Referring to Question #7, find the standard deviation. Round your answer to four decimal places.

Referring to Question #7, would it be unusual for a student to get 60% or better? Why or why not?

Explanation / Answer

a.
Mean ( np ) =50 * 0.25 = 12.5
Standard Deviation ( npq )= 50*0.25*0.75 = 3.0619
Normal Distribution = Z= X- u / sd                   
b.
Normal Distribution
Proportion ( P ) =0.03
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.03*0.97/0.25)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 0.6) = (0.6-0.03)/0.3412
= 0.57/0.3412 = 1.6706
= P ( Z >1.671) From Standard Normal Table
= 0.0474                     
which is less than 0.05% we consider to be unusual

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