The average production cost for major movies is 69 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 18 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 69]] 21 b. What is the distribution of ? - N( 69 4.9497 c. For a single randomly selected movie, find the probability that this movie's production cost is between 65 and 69 million dollars. d. For the group of 18 movies, find the probability that the average production cost is between 65 and 69 million dollars. e. For part d), is the assumption of normal necessary? No Yes o
The average production cost for major movies is 69 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 18 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 69]] 21 b. What is the distribution of ? - N( 69 4.9497 c. For a single randomly selected movie, find the probability that this movie's production cost is between 65 and 69 million dollars. d. For the group of 18 movies, find the probability that the average production cost is between 65 and 69 million dollars. e. For part d), is the assumption of normal necessary? No Yes o
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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![**Title: Understanding the Distribution of Movie Production Costs**
The average production cost for major movies is 69 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 18 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible.
---
**a. What is the distribution of \( X \)?**
\[ X \sim N(69, 21) \]
**b. What is the distribution of \( \bar{x} \)?**
\[ \bar{x} \sim N \left(69, \frac{21}{\sqrt{18}}\right) \]
\[ \bar{x} \sim N(69, 4.9497) \]
---
**c. For a single randomly selected movie, find the probability that this movie's production cost is between 65 and 69 million dollars.**
\[ \Pr(65 < X < 69) = \text{(Answer required)} \]
---
**d. For the group of 18 movies, find the probability that the average production cost is between 65 and 69 million dollars.**
\[ \Pr(65 < \bar{x} < 69) = \text{(Answer required)} \]
---
**e. For part d), is the assumption of normal necessary?**
\[ \text{Yes} \]
---
In the equations above:
- \( X \) represents the production cost of a single movie.
- \( \bar{x} \) represents the average production cost of the 18 selected movies.
- \( N(\mu, \sigma) \) denotes a normal distribution with mean \( \mu \) and standard deviation \( \sigma \).
This problem involves understanding key concepts of normal distribution and the impact of sample size on the standard deviation of the sample mean.
**Graphs and Diagrams:**
There are no graphs or diagrams in the provided text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed8faccd-6cf6-4e70-b90c-dd265de0d7ab%2Fced28323-9175-4163-ace7-b3fe0a5debdb%2Fr8xgpg_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding the Distribution of Movie Production Costs**
The average production cost for major movies is 69 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 18 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible.
---
**a. What is the distribution of \( X \)?**
\[ X \sim N(69, 21) \]
**b. What is the distribution of \( \bar{x} \)?**
\[ \bar{x} \sim N \left(69, \frac{21}{\sqrt{18}}\right) \]
\[ \bar{x} \sim N(69, 4.9497) \]
---
**c. For a single randomly selected movie, find the probability that this movie's production cost is between 65 and 69 million dollars.**
\[ \Pr(65 < X < 69) = \text{(Answer required)} \]
---
**d. For the group of 18 movies, find the probability that the average production cost is between 65 and 69 million dollars.**
\[ \Pr(65 < \bar{x} < 69) = \text{(Answer required)} \]
---
**e. For part d), is the assumption of normal necessary?**
\[ \text{Yes} \]
---
In the equations above:
- \( X \) represents the production cost of a single movie.
- \( \bar{x} \) represents the average production cost of the 18 selected movies.
- \( N(\mu, \sigma) \) denotes a normal distribution with mean \( \mu \) and standard deviation \( \sigma \).
This problem involves understanding key concepts of normal distribution and the impact of sample size on the standard deviation of the sample mean.
**Graphs and Diagrams:**
There are no graphs or diagrams in the provided text.
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