Question

Extra Practice / Homework 5) You are taking a multiple choice quiz which consists of 6 questions. Each question has five possible answers to choose from of which only one is correct. Answer the following questions a) What is your chance of choosing the correct answer for any particular problem? (express as a decimal rounded to two decimal places.) b) Explain how you could use your calculator to generate and use random numbers to simulate guessing on the each question of the quiz. c) Conduct a simulation with 20 trials indicating what random numbers were used and how many correct answers you got for each trial. d) Use your simulation to estimate for the probability of getting exactly one correct answer on the quiz if you guessed at all questions. e) Use your simulation to estimate for the probability of getting a score of less than 33.33% (fewer than 2 of 6 correct) on the quiz.

Trial Components Outcomes

Answer 1

There are 6 question in the multiple choice test.

While each question have five possible answers out of which only one is correct.

a) The probability of choosing the correct answer for any particular problem is given by

p=1/5=0.20

b) Since every question may be correct or incorrect. Therefore this is a bernoullian experiment with p=0.20, while there are 6 question.

Therefore the distribution of the number of correct question is a Binomial distribution with n=6 and p=0.20

By using this value of the parameter we perform the simulation.

c) ### By using R:

> n=6
> p=0.20
> x=rbinom(20,n,p) ###command to generate random sample
> x
[1] 3 1 2 0 1 0 1 1 2 2 1 3 3 0 0 1 1 0 1 2

d) the probability of getting exactly one correct answer on the quiz if you guessed at all questions is given by:

P(X=1)

## By using R

> table(x)
x
0 1 2 3
5 8 4 3

e) the probability of getting a score of less than 33.33% or fewer than 2

Is given by: