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Suppose the movie theatre box office of a new film to be released is predicted to follow a Normal distribution, with mean equals 100 million dollars and standard deviation equals 20 million dollars. What is the probability that the box office will be at least 70 million? What is the probability that the box office will be either more than 70 million or less than 40 million dollars? There is 80% probability that the box office will be greater than or equal to million. (NOTE: Round your answers to 2 decimal places. Do not type in any non-integer symbol or text other than decimal.)

Suppose the movie theatre box office of a new film to be released is predicted to follow a Normal distribution, with mean equals 100 million dollars and standard deviation equals 20 million dollars. What is the probability that the box office will be at least 70 million? What is the probability that the box office will be either more than 70 million or less than 40 million dollars? There is 80% probability that the box office will be greater than or equal to million. (NOTE: Round your answers to 2 decimal places. Do not type in any non-integer symbol or text other than decimal.)

MATLAB: An Introduction with Applications
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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### Normal Distribution and Box Office Prediction Analysis **Scenario:** Suppose the movie theatre box office of a new film to be released is predicted to follow a Normal distribution, with the mean equals 100 million dollars and the standard deviation equals 20 million dollars. --- **Questions:** 1. **What is the probability that the box office will be at least 70 million?** - Answer: [Text Box for Input] 2. **What is the probability that the box office will be either more than 70 million or less than 40 million dollars?** - Answer: [Text Box for Input] 3. **There is 80% probability that the box office will be greater than or equal to ___ million.** - Answer: [Text Box for Input] (Note: Round your answers to 2 decimal places. Do not type in any non-integer symbol or text other than decimal.) --- **Explanation:** To solve the problems, use the properties of the normal distribution: - **Normal Distribution:** It is symmetric and bell-shaped, defined by its mean (μ = 100 million dollars) and standard deviation (σ = 20 million dollars). - **Calculations:** - Use Z-scores to relate the probabilities and make calculations easier. - Transform the original normal distribution into the standard normal distribution (mean 0 and standard deviation 1) to find probabilities from Z-tables. _For additional support in calculus and transformations, consider reviewing materials on Normal Distribution and Z-score calculations._
Transcribed Image Text:### Normal Distribution and Box Office Prediction Analysis **Scenario:** Suppose the movie theatre box office of a new film to be released is predicted to follow a Normal distribution, with the mean equals 100 million dollars and the standard deviation equals 20 million dollars. --- **Questions:** 1. **What is the probability that the box office will be at least 70 million?** - Answer: [Text Box for Input] 2. **What is the probability that the box office will be either more than 70 million or less than 40 million dollars?** - Answer: [Text Box for Input] 3. **There is 80% probability that the box office will be greater than or equal to ___ million.** - Answer: [Text Box for Input] (Note: Round your answers to 2 decimal places. Do not type in any non-integer symbol or text other than decimal.) --- **Explanation:** To solve the problems, use the properties of the normal distribution: - **Normal Distribution:** It is symmetric and bell-shaped, defined by its mean (μ = 100 million dollars) and standard deviation (σ = 20 million dollars). - **Calculations:** - Use Z-scores to relate the probabilities and make calculations easier. - Transform the original normal distribution into the standard normal distribution (mean 0 and standard deviation 1) to find probabilities from Z-tables. _For additional support in calculus and transformations, consider reviewing materials on Normal Distribution and Z-score calculations._
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