Ken and Lucas are two friends who say they have no previous knowledge of statistics. They are going to take a placement test to see if they should start at the introductory level or not.

The placement test is a multiple-choice test with 56 questions. Each question has 5 multiple-choice options with exactly one correct answer.

What is the expected number (mean) of correct answers if a student were to randomly guess?(Do not round)

What is the standard deviation for the number of correct answers if a student were to randomly guess?(Round to two decimal places)

The usual number of correct answers, if a student were to randomly guess, would beto. (Round to the nearest whole number that would be within the interval.)

What is the probability of getting 12 or more questions correct if you are randomly guessing?(Round to four decimal places.)

What is the probability of getting 28 or more questions correct if you are randomly guessing?(Round to four decimal places.)

Ken got 12 questions correct.

Lucas got 28 questions correct.

Is it reasonable to believe that Ken had no prior knowledge of statistics?

• yes
• no

Why or why not?

Is it reasonable to believe that Lucas had no prior knowledge of statistics?

• yes
• no

Why or why not?