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2. (Mean or Expected Value) In a lottery, there are 25 prizes of $5, 5 prizes of $25, and one prize of $100. Assuming that 1,000 tickets are to be issued and sold, what is a fair price (i.e. for zero profit) to charge to break even? Use the following blank table.

2. (Mean or Expected Value) In a lottery, there are 25 prizes of $5, 5 prizes of $25, and one prize of $100. Assuming that 1,000 tickets are to be issued and sold, what is a fair price (i.e. for zero profit) to charge to break even? Use the following blank table.

MATLAB: An Introduction with Applications
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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answers to part 2 and part 3 (d)

### Expected Values and Binomial Distribution #### 2. Mean or Expected Value In a lottery, there are: - 25 prizes of $5, - 5 prizes of $25, and - one prize of $100. Assuming that 1,000 tickets are to be issued and sold, what is a fair price (i.e., for zero profit) to charge to break even? Use the following blank table: | X | P(X) | |---|-----------| | | | | | | | | | #### 3. Binomial Distribution There are 100 multiple choice questions on an exam, each having responses a, b, c, or d. Suppose each student has a probability \( p \) of correctly answering a question chosen at random from a universe of possible questions. In addition, the answers from question to question are independent. Let random variable \( X \) be the number of questions for which the student answers correctly. - **Expression:** \( X \sim B(n, p) \text{; } X = B(n = 100, p = 1/4) \) ##### Questions: **(a) We can see the distribution of \( X \) is a Binomial distribution with \( n \) and \( p \). What are \( n \) and \( p \)?** **(b) What is the probability that the student will score exactly 25 of 100 points? (If possible, use Excel function, "binom.dist")** - Answer: 0.091799692 **(c) What is the probability that the student will score more than 25 points? (If possible, use Excel function, "binom.dist")** - Answer: 0.446529176 **(d) On average, how many points will the student score?**
Transcribed Image Text:### Expected Values and Binomial Distribution #### 2. Mean or Expected Value In a lottery, there are: - 25 prizes of $5, - 5 prizes of $25, and - one prize of $100. Assuming that 1,000 tickets are to be issued and sold, what is a fair price (i.e., for zero profit) to charge to break even? Use the following blank table: | X | P(X) | |---|-----------| | | | | | | | | | #### 3. Binomial Distribution There are 100 multiple choice questions on an exam, each having responses a, b, c, or d. Suppose each student has a probability \( p \) of correctly answering a question chosen at random from a universe of possible questions. In addition, the answers from question to question are independent. Let random variable \( X \) be the number of questions for which the student answers correctly. - **Expression:** \( X \sim B(n, p) \text{; } X = B(n = 100, p = 1/4) \) ##### Questions: **(a) We can see the distribution of \( X \) is a Binomial distribution with \( n \) and \( p \). What are \( n \) and \( p \)?** **(b) What is the probability that the student will score exactly 25 of 100 points? (If possible, use Excel function, "binom.dist")** - Answer: 0.091799692 **(c) What is the probability that the student will score more than 25 points? (If possible, use Excel function, "binom.dist")** - Answer: 0.446529176 **(d) On average, how many points will the student score?**
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