The average production cost for major movies is 62 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 49 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( 62 18 b. What is the distribution of ? a N( 62 2.5714 c. For a single randomly selected movie, find the probability that this movie's production cost is between 61 and 63 million dollars. d. For the group of 49 movies, find the probability that the average production cost is between 61 and 63 million dollars. e. For part d), is the assumption of normal necessary? Yes No Hint: Some Helpful Videos: Finding the Sampling Distribution [+] Finding a Probability Using the Central Limit Theorem [+] Finding Value Given a Probability Using the Central Limit Theorem [+] • The Central Limit Theorem For Sums [+] Hint

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The average production cost for major movies is 62 million dollars and the standard deviation is 18 million
dollars. Assume the production cost distribution is normal. Suppose that 49 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 62
18
b. What is the distribution of x? a - N( 62
2.5714
c. For a single randomly selected movie, find the probability that this movie's production cost is
between 61 and 63 million dollars.
d. For the group of 49 movies, find the probability that the average production cost is between 61 and
63million dollars.
e. For part d), is the assumption of normal necessary? O YesO No
Hint:
Some Helpful Videos:
Finding the Sampling Distribution [+]
Finding a Probability Using the Central Limit Theorem [+]
Finding Value Given a Probability Using the Central Limit Theorem [+]
• The Central Limit Theorem For Sums [+]
Hint
Transcribed Image Text:The average production cost for major movies is 62 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 49 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 62 18 b. What is the distribution of x? a - N( 62 2.5714 c. For a single randomly selected movie, find the probability that this movie's production cost is between 61 and 63 million dollars. d. For the group of 49 movies, find the probability that the average production cost is between 61 and 63million dollars. e. For part d), is the assumption of normal necessary? O YesO No Hint: Some Helpful Videos: Finding the Sampling Distribution [+] Finding a Probability Using the Central Limit Theorem [+] Finding Value Given a Probability Using the Central Limit Theorem [+] • The Central Limit Theorem For Sums [+] Hint
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