Question

Morgan and Alejandra 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 94 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 be________ to _____ . (Round to the nearest whole number that would be within the interval.)

What is the probability of getting 16 or more questions correct if you are randomly guessing?  (Round to four decimal places.)

What is the probability of getting 45 or more questions correct if you are randomly guessing?  (Round to four decimal places.)

Morgan got 16 questions correct.

Alejandra got 45 questions correct.

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

• yes
• no

Why or why not?

Answer 1

The number of correct answers out of 94 has Binomial distribution with .

The PMF of is .

a) The expected value of the distribution is

b)The variance is

c)The usual number of correct answers, if a student were to randomly guess, would be___18_____ to __19___ .

d)The probability of getting 16 or more questions correct if you are randomly guessing is

e)The probability of getting 45 or more questions correct if you are randomly guessing is

f) Yes. Since , 16 or more correct has 80% chance.