Jane and Sophia 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 88 questions. Each question has 4 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 be 14 to 30 . (Round to the nearest whole number that would be within the interval.)

What is the probability of getting 19 or more questions correct if you are randomly guessing?

(Round to four decimal places.)

What is the probability of getting 51 or more questions correct if you are randomly guessing?

(Round to four decimal places.)

Jane got 19 questions correct.

Sophia got 51 questions correct.

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

• yes
• no

Why or why not?

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

• yes
• no

Why or why not?