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.

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**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.
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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