2. A company may makes infant, toddler, or child toys and the sales will be effected by which of three cartoons get the highest ratings. Show A has a 0.3 probability or getting the highest rating, Show B has 0.4, and Show C has 0.3. They payoffs are in the table below. Show A Show B Show C Infant 7 -2 6. Toddler -3 8. -1 Child 2 -4 8

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
### Problem Statement

A company that manufactures toys for infants, toddlers, and children wants to evaluate how the sales of their products will be affected by the ratings of three different TV shows. Each show has a specific probability of receiving the highest rating, and the impact of each show on toy sales is given in a payoff matrix.

### Probabilities of Getting the Highest Rating

- **Show A**: 0.3 probability
- **Show B**: 0.4 probability
- **Show C**: 0.3 probability

### Payoff Matrix

The table below illustrates the potential sales impact (payoffs) for each type of toy (infant, toddler, and child) based on which TV show receives the highest rating.

|        | Show A | Show B | Show C |
|--------|--------|--------|--------|
| Infant |      7 |     -2 |      6 |
| Toddler|     -3 |      8 |     -1 |
| Child  |      2 |     -4 |      8 |

### Explanation of the Payoff Matrix

- **Infant Toys**
  - Show A: Sales impact of 7
  - Show B: Sales impact of -2
  - Show C: Sales impact of 6

- **Toddler Toys**
  - Show A: Sales impact of -3
  - Show B: Sales impact of 8
  - Show C: Sales impact of -1

- **Child Toys**
  - Show A: Sales impact of 2
  - Show B: Sales impact of -4
  - Show C: Sales impact of 8

This payoff matrix can be used to determine the expected impact on toy sales by calculating the weighted average based on the probabilities of each show receiving the highest rating. This type of analysis can aid the company in strategic decision-making regarding which product lines to focus on or market more extensively based on television show ratings.
Transcribed Image Text:### Problem Statement A company that manufactures toys for infants, toddlers, and children wants to evaluate how the sales of their products will be affected by the ratings of three different TV shows. Each show has a specific probability of receiving the highest rating, and the impact of each show on toy sales is given in a payoff matrix. ### Probabilities of Getting the Highest Rating - **Show A**: 0.3 probability - **Show B**: 0.4 probability - **Show C**: 0.3 probability ### Payoff Matrix The table below illustrates the potential sales impact (payoffs) for each type of toy (infant, toddler, and child) based on which TV show receives the highest rating. | | Show A | Show B | Show C | |--------|--------|--------|--------| | Infant | 7 | -2 | 6 | | Toddler| -3 | 8 | -1 | | Child | 2 | -4 | 8 | ### Explanation of the Payoff Matrix - **Infant Toys** - Show A: Sales impact of 7 - Show B: Sales impact of -2 - Show C: Sales impact of 6 - **Toddler Toys** - Show A: Sales impact of -3 - Show B: Sales impact of 8 - Show C: Sales impact of -1 - **Child Toys** - Show A: Sales impact of 2 - Show B: Sales impact of -4 - Show C: Sales impact of 8 This payoff matrix can be used to determine the expected impact on toy sales by calculating the weighted average based on the probabilities of each show receiving the highest rating. This type of analysis can aid the company in strategic decision-making regarding which product lines to focus on or market more extensively based on television show ratings.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman