Math 104.03. Spring 2017. Assignment 6, due Thursday March 30 at 11pm 2. Adam an

Question

Math 104.03. Spring 2017. Assignment 6, due Thursday March 30 at 11pm 2. Adam and Bono are classmates, and passing the exam in their class requires answering at least 2ry of the questions conrectly. This problem investigates whether a student has a beterchance of passing a shorter exam or a longer one. Intuitively, what do you think? Suppose that Adam has studied hard. and for each question, has an 80% chance of answering correctly a. What is the probability that Adam will pass the exam if it has 6 questions? Write out the full expression you need to compute in order to find this probability, and compute the value. b. what is the probability that Adam will pass the exam ifit has 9 questions? write out the full expression you need to compute in order to find this probability, and compute the value.

Explanation / Answer

Question 2

Part a

We are given, n = 6 and p = 0.8

Passing Criterion = 2/3 of the questions correctly

For n =6, (2/3)*6 = 4 questions need to solve correctly for passing the exam.

This means we have to find P(X=4)

We have to use binomial distribution. The formula for binomial distribution is given as below:

P(X=x) = nCx*p^x*q^(n – x)

Where, q = 1 – p = 1 – 0.8 = 0.2

P(X=4) = 6C4*0.8^4*0.2^2

P(X=4) = 0.24576

Required probability = 0.24576

Part b

We are given, n = 9 and p = 0.8

Passing Criterion = 2/3 of the questions correctly

For n =9, (2/3)*9 = 6 questions need to solve correctly for passing the exam.

This means we have to find P(X=6)

We have to use binomial distribution. The formula for binomial distribution is given as below:

P(X=x) = nCx*p^x*q^(n – x)

Where, q = 1 – p = 1 – 0.8 = 0.2

P(X=6) = 9C6*0.8^6*0.2^3

P(X=6) = 0.176161

Required probability = 0.176161

Part c

We are given, n = 6 and p = 0.55

Passing Criterion = 2/3 of the questions correctly

For n =6, (2/3)*6 = 4 questions need to solve correctly for passing the exam.

This means we have to find P(X=4)

We have to use binomial distribution. The formula for binomial distribution is given as below:

P(X=x) = nCx*p^x*q^(n – x)

Where, q = 1 – p = 1 – 0.55 = 0.45

P(X=4) = 6C4*0.55^4*0.45^2

P(X=4) = 0.27795

Required probability = 0.27795

Part d

We are given, n = 9 and p = 0.55

Passing Criterion = 2/3 of the questions correctly

For n =9, (2/3)*9 = 6 questions need to solve correctly for passing the exam.

This means we have to find P(X=6)

We have to use binomial distribution. The formula for binomial distribution is given as below:

P(X=x) = nCx*p^x*q^(n – x)

Where, q = 1 – p = 1 – 0.55 = 0.45

P(X=6) = 9C6*0.55^6*0.45^3

P(X=6) = 0.211881

Required probability = 0.211881

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