The table below shows the highest grossing movies of the given year. The amount is the domestic box office gross, in millions of dollars. Year Movie Amount (millions) 2006 Pirates of the Caribbean: Dead Man's Chest 423.32 2007 Spider-Man 3 336.53 2008 The Dark Knight 533.35 2009 Avatar 760.51 2010 Toy Story 3 415.00 2011 Harry Potter and the Deathly Hallows: Part 2 381.01 2012 The Avengers 623.28 2013 The Hunger Games: Catching Fire 424.67 2014 American Sniper 350.13 Let M = M(y) denote the highest grossing movie in year y, and let B = B(y) denote the gross for that movie. (a) Give the values of M(2014) and B(2014). M(2014) = ---Select--- Pirates of the Caribbean: Dead Man's Chest Spider-Man 3 The Dark Knight Avatar Toy Story 3 Harry Potter and the Deathly Hallows: Part 2 The Avengers The Hunger Games: Catching Fire American Sniper B(2014) = $ million (b) Use functional notation to indicate the amount for the movie with the highest gross in 2012.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The table below shows the highest grossing movies of the given year. The amount is the domestic box office gross, in millions of dollars.
| Year | Movie | Amount (millions) |
|---|---|---|
| 2006 | Pirates of the Caribbean: Dead Man's Chest |
423.32 |
| 2007 | Spider-Man 3 | 336.53 |
| 2008 | The Dark Knight | 533.35 |
| 2009 | Avatar | 760.51 |
| 2010 | Toy Story 3 | 415.00 |
| 2011 | Harry Potter and the Deathly Hallows: Part 2 |
381.01 |
| 2012 | The Avengers | 623.28 |
| 2013 | The Hunger Games: Catching Fire |
424.67 |
| 2014 | American Sniper | 350.13 |
Let
denote the highest grossing movie in year y, and let
denote the gross for that movie.
| M(2014) | = ---Select--- Pirates of the Caribbean: Dead Man's Chest Spider-Man 3 The Dark Knight Avatar Toy Story 3 Harry Potter and the Deathly Hallows: Part 2 The Avengers The Hunger Games: Catching Fire American Sniper |
| B(2014) | = $ million |
(b) Use
Given information:
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