The average production cost for major movies is 67 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 12 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-NO b. What is the distribution of ? ~ N( c. For a single randomly selected movie, find the probability that this movie's production cost is between 68 and 70 million dollars.
The average production cost for major movies is 67 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 12 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-NO b. What is the distribution of ? ~ N( c. For a single randomly selected movie, find the probability that this movie's production cost is between 68 and 70 million dollars.
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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![**Text for Educational Website**
The average production cost for major movies is 67 million dollars, with a standard deviation of 18 million dollars. Assume the production cost distribution is normal. Suppose that 12 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 \( X \)? \( X \sim N( \) [blank] , [blank] \( ) \)
b. What is the distribution of \( \bar{X} \)? \( \bar{X} \sim N( \) [blank] , [blank] \( ) \)
c. For a single randomly selected movie, find the probability that this movie's production cost is between 68 and 70 million dollars.
[blank]
d. For the group of 12 movies, find the probability that the average production cost is between 68 and 70 million dollars.
[blank]
e. For part d), is the assumption of normal necessary?
○ No ○ Yes
**Explanation of Diagram:**
The image is a set of statistical questions related to the normal distribution of movie production costs. There are no graphs or diagrams present. The questions focus on understanding and applying the properties of normal distribution and sampling distribution to calculate probabilities and determine the necessity of normal distribution assumptions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7248d714-2630-4255-aa39-67ac8596a103%2F3bef37a1-0d66-4f53-9171-9ce16c36c27e%2Fg4s6rf9_processed.png&w=3840&q=75)
Transcribed Image Text:**Text for Educational Website**
The average production cost for major movies is 67 million dollars, with a standard deviation of 18 million dollars. Assume the production cost distribution is normal. Suppose that 12 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 \( X \)? \( X \sim N( \) [blank] , [blank] \( ) \)
b. What is the distribution of \( \bar{X} \)? \( \bar{X} \sim N( \) [blank] , [blank] \( ) \)
c. For a single randomly selected movie, find the probability that this movie's production cost is between 68 and 70 million dollars.
[blank]
d. For the group of 12 movies, find the probability that the average production cost is between 68 and 70 million dollars.
[blank]
e. For part d), is the assumption of normal necessary?
○ No ○ Yes
**Explanation of Diagram:**
The image is a set of statistical questions related to the normal distribution of movie production costs. There are no graphs or diagrams present. The questions focus on understanding and applying the properties of normal distribution and sampling distribution to calculate probabilities and determine the necessity of normal distribution assumptions.
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