The following table gives the 2012 total payroll (in millions of dollars) and the percentage of games won during the 2012 season by each of the National League baseball teams.| Team | Total Payroll (millions of dollars) | Runs Scored ||-----------------------|-------------------------------------|-------------|| Arizona Diamondbacks | 83 | 46 || Atlanta Braves | 89 | 35 || Chicago Cubs | 110 | 57 || Cincinnati Reds | 111 | 34 || Colorado Rockies | 93 | 39 || Los Angeles Dodgers | 264 | 51 || Miami Marlins | 59 | 38 || Milwaukee Brewers | 99 | 39 || New York Mets | 95 | 53 || Philadelphia Phillies | 127 | 33 || Pittsburgh Pirates | 82 | 58 || San Diego Padres | 92 | 40 || San Francisco Giants | 164 | 46 || St. Louis Cardinals | 112 | 59 || Washington Nationals | 156 | 45 |The least squares regression line is $\mu_y = 41.073 + 0.033x$, where $x$ = total payroll (in millions of dollars) and $y$ = percentage of games won.Predict the percentage of games won by a team with a total payroll of $87 million.Round your answer to the nearest integer.\[\boxed{} \quad \% \]

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The following table gives the 2012 total payroll (in millions of dollars) and the percentage of games won during the 2012 season by each of the National League baseball teams. Total Payroll (millions of dollars) Runs Scored Team Arizona Diamondbacks 83 46 Atlanta Braves Chicago Cubs Cincinnati Reds Colorado Rockies 89 35 110 57 II 34 93 39 Los Angeles Dodgers 264 51 Miami Marlins Milwaukee Brewers New York Mets 59 38 99 39 95 53 Philadelphia Phillies 127 33 Pittsburgh Pirates 82 58 San Diego Padres San Francisco Giants 92 40 164 46 St. Louis Cardinals 112 59 Washington Nationals 156 45 The least squares regression line is 4yly = 41.073 + 0.033x, wherex =total payroll (in millions of dollars) and y = percentage of games won. Predict the percentage of games won by a team with a total payroll of $87 million. Round your answer to the nearest integer.

The following table gives the 2012 total payroll (in millions of dollars) and the percentage of games won during the 2012 season by each of the National League baseball teams. Total Payroll (millions of dollars) Runs Scored Team Arizona Diamondbacks 83 46 Atlanta Braves Chicago Cubs Cincinnati Reds Colorado Rockies 89 35 110 57 II 34 93 39 Los Angeles Dodgers 264 51 Miami Marlins Milwaukee Brewers New York Mets 59 38 99 39 95 53 Philadelphia Phillies 127 33 Pittsburgh Pirates 82 58 San Diego Padres San Francisco Giants 92 40 164 46 St. Louis Cardinals 112 59 Washington Nationals 156 45 The least squares regression line is 4yly = 41.073 + 0.033x, wherex =total payroll (in millions of dollars) and y = percentage of games won. Predict the percentage of games won by a team with a total payroll of $87 million. Round your answer to the nearest integer.

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Concept explainers

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.

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The following table gives the 2012 total payroll (in millions of dollars) and the percentage of games won during the 2012 season by each of the National League baseball teams.

| Team | Total Payroll (millions of dollars) | Runs Scored |
|-----------------------|-------------------------------------|-------------|
| Arizona Diamondbacks | 83 | 46 |
| Atlanta Braves | 89 | 35 |
| Chicago Cubs | 110 | 57 |
| Cincinnati Reds | 111 | 34 |
| Colorado Rockies | 93 | 39 |
| Los Angeles Dodgers | 264 | 51 |
| Miami Marlins | 59 | 38 |
| Milwaukee Brewers | 99 | 39 |
| New York Mets | 95 | 53 |
| Philadelphia Phillies | 127 | 33 |
| Pittsburgh Pirates | 82 | 58 |
| San Diego Padres | 92 | 40 |
| San Francisco Giants | 164 | 46 |
| St. Louis Cardinals | 112 | 59 |
| Washington Nationals | 156 | 45 |

The least squares regression line is $\mu_y = 41.073 + 0.033x$, where $x$ = total payroll (in millions of dollars) and $y$ = percentage of games won.

Predict the percentage of games won by a team with a total payroll of $87 million.

Round your answer to the nearest integer.

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