**I WILL RATE AND LEAVE FEEDBACK :)**

Question 1: Cameron and Carlos 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 55 questions. Each question has 5 multiple-choice options with exactly one correct answer.

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

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

c) 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.)

d) What is the probability of getting 10 or more questions correct if you are randomly guessing? _______(Round to four decimal places.)

e) What is the probability of getting 31 or more questions correct if you are randomly guessing?______(Round to four decimal places.)

Cameron got 10 questions correct.

Carlos got 31 questions correct.

f) Is it reasonable to believe that Cameron had no prior knowledge of statistics?Yes or no? Why or why not?

g) Is it reasonable to believe that Carlos had no prior knowledge of statistics? Yes or no? Why or why not?

Question 2: Eduardo is the general manager for a business. One of Eduardo's tasks is to assign extra projects to his employees. These extra projects are supposed to be assigned following a particular order. The extra projects result in additional pay, so the employees are concerned that the extra projects are assigned following the proper procedure. Errors do happen though. Eduardo makes an error once every 100 tasks that he assigns.

a) If Eduardo were to assign 10 tasks, what is the probability that he would make 3 or more mistakes?______(Round your answer to six decimal places.)

b) When Eduardo was supposed to assign 10 tasks to Amanda, he DID make 3 mistakes. Was Amanda treated fairly? Yes or no?

c) What conclusions could you make about the three mistakes? Make sure to explain your conclusion thoroughly.