test107_sol

# test107_sol - Midterm 1 1 In a multiple-choice test a...

This preview shows pages 1–2. Sign up to view the full content.

Midterm 1 1. In a multiple-choice test, a student can answer any question correctly with probability of 0.85, independently of all other questions. The test consists of 100 questions. Each correct answer is worth 4 points, and for each incorrect answer 1 point is deducted. This student always answers all the questions. a) What is the student’s expected score (in points)? b) What is the probability of the student’s score dropping below 275 points? Hint: use normal approximation. c) What is the probability of the student obtaining more than 350 points on the test? Solution. If we denote by X the number of questions that the students answers correctly, and by Q his score in points, then, obviously, X and Q are related by P = 4 X - (100 - X ) = 5 X - 100. a) Clearly, X Bin (100 , 0 . 85). Therefore, E ( Q ) = 5 E ( X ) - 100 = 5 · 100 · 0 . 85 - 100 = 325. b) Pr( Q < 275) = Pr( X < 75) = Pr( X 74) Pr Z < 74 . 5 - 85 100 · 0 . 85 · 0 . 15 · = Φ( - 2 . 66) = 0 . 0016. c) Pr( Q < 350) = Pr( X > 90) = Pr( X 91) Pr Z > 90 . 5 - 85 100 · 0 . 85 · 0 . 15 · = 1 - Φ(1 . 54) = 0 . 062.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern