8. A multiple-choice quiz consists of 20 questions, each with 4 possible answers. Find the mean for the number of correct answers if a student guesses on each question. Find the probability of exactly 16 correct answers.
8. A multiple-choice quiz consists of 20 questions, each with 4 possible answers. Find the mean for the number of correct answers if a student guesses on each question. Find the probability of exactly 16 correct answers.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Question 8: Probability and Statistics**
A multiple-choice quiz consists of 20 questions, each with 4 possible answers.
1. **Find the Mean for the Number of Correct Answers:**
- Assume a student guesses on each question.
2. **Probability Calculation:**
- Find the probability of exactly 16 correct answers.
*Explanation:*
- Since each question has 4 possible answers, the probability of choosing the correct answer by guessing is \( \frac{1}{4} \).
- The scenario described is a binomial distribution, where \( n = 20 \) (total questions) and \( p = \frac{1}{4} \) (probability of a correct answer).
- To determine the mean number of correct answers, use the formula for the expected value of a binomial distribution: \( E(X) = n \times p \).
- To calculate the probability of exactly 16 correct answers, use the binomial probability formula.
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