The average production cost for major movies is 69 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 8 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N   What is the distribution of ¯xx¯? ¯xx¯ ~ N For a single randomly selected movie, find the probability that this movie's production cost is between 64 and 70 million dollars.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The average production cost for major movies is 69 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 8 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

  1. What is the distribution of XX? XX ~ N  
  2. What is the distribution of ¯xx¯? ¯xx¯ ~ N
  3. For a single randomly selected movie, find the probability that this movie's production cost is between 64 and 70 million dollars. 
  4. For the group of 8 movies, find the probability that the average production cost is between 64 and 70 million dollars. 
  5. For part d), is the assumption of normal necessary?
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