answers to part 2 and part 3 (d) ### Expected Values and Binomial Distribution#### 2. Mean or Expected ValueIn 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 DistributionThere 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?**

2. It is given that there are 25 prices of $5, 5 prizes of $25 and 1 prize of $100. Thus, the random…

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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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?**

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