The average production cost for major movies is 58 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 41 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( b. What is the distribution of x? ~ N( c. For a single randomly selected movie, find the probability that this movie's production cost is between 54 and 59 million dollars.

The average production cost for major movies is 58 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 41 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( b. What is the distribution of x? ~ N( c. For a single randomly selected movie, find the probability that this movie's production cost is between 54 and 59 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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Question

I need help with this problem.

The average production cost for major movies is 58 million dollars and the standard deviation is 20 million
dollars. Assume the production cost distribution is normal. Suppose that 41 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 x? x NO
c. For a single randomly selected movie, find the probability that this movie's production cost is
between 54 and 59 million dollars.
d. For the group of 41 movies, find the probability that the average production cost is between 54 and
59 million dollars.
e. For part d), is the assumption of normal necessary? No Yes

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Follow-up Questions

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Follow-up Question

I need help with the last few questions.

The average production cost for major movies is 58 million dollars, with a standard deviation of 20 million dollars. Assuming the production cost distribution is normal, 41 randomly selected major movies are analyzed. Here are the details:

a. Distribution of $ X $:
\[
X \sim N(58, 20)
\]

b. Distribution of $ \bar{x} $:
\[
\bar{x} \sim N\left(58, \frac{20}{\sqrt{41}}\right) \approx N(58, 3.1235)
\]

c. Probability for a single randomly selected movie to have a production cost between 54 and 59 million dollars:
\[
0.5254
\]

d. Probability for the average production cost of the 41 movies to fall between 54 and 59 million dollars:
\[
\text{(answer not provided in the image)}
\]

e. Is the assumption of normality necessary for part d)?
\[
\text{Yes}
\]

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