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805+ Level|   Graphs|   Math Related|      
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The graph is a frequency distribution of the earned run averages (ERA) 17 Dec 2023, 01:54
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Dropdown 1: greater than Dropdown 2: 0.5
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Data Insights (DI) Butler 2023-24 [Question #157, Date: Dec-15-2023] [Click here for Details]



The graph is a frequency distribution of the earned run averages (ERA) of 92 qualifying pitchers at the end of the 2011 Major League Baseball season. The data are plotted separately for pitchers in the two leagues (the National League and the American League) that make up Major League Baseball. So, for example, 2 American League pitchers and 3 National League pitchers had an ERA between 2.00 and 2.49, inclusive, for a total of 5 Major League Baseball pitchers with an ERA between 2.00 and 2.49.

Based on the given information, fill in the blanks in each of the following statements.

1. Among the qualifying pitchers, the probability that an American League pitcher had an ERA between 2.00 and 2.49 is the probability that a National League pitcher had an ERA greater than 4.99.

2. If a pitcher had an ERA between 2.00 and 2.99 inclusive, then the probability that he was a National League pitcher is .

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Dropdown 1: greater than Dropdown 2: 0.5
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The graph is a frequency distribution of the earned run averages (ERA) 18 Dec 2023, 03:02
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Please provide an explanation to this question.

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The graph is a frequency distribution of the earned run averages (ERA) 18 Dec 2023, 08:40
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Statement 2 :If a pitcher had an ERA between 2.00 and 2.99 inclusive, then the probability that he was a National League pitcher is ____
=>
Total no. of pitcher who had an ERA between 2.00 and 2.99 inclusive = Total no. of pitcher who had an ERA between 2.00 and 2.4 and between 2.50 and 2.99 (the National League + the American League)
=> 6+5+2+3= 16
=> among this 16 pitchers National League pitchers are = (5+3)=8
=> probability = 8/16= 1/2= 0.5
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The graph is a frequency distribution of the earned run averages (ERA) 18 Dec 2023, 15:06
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Official Explanation

Two American League pitchers had an ERA between 2.00 and 2.49, and two National League pitchers had an ERA greater than 4.99. However, it looks like more National League pitchers than American League pitchers are included in the graph and, if you count you’ll find 50 National League pitchers and 42 American League pitchers. So, the probability that an American League pitcher had an ERA between 2.00 and 2.49 is 2 out of 42, which is greater than2 out of 50, the probability that a National League pitcher had an ERA greater than 4.99.

The correct answer is (C).

Two American League pitchers and three National League pitchers had an ERA between 2.00 and 2.49. Six American League pitchers and five National League pitchers had an ERA between 2.50 and 2.99. In total, 16 pitchers—eight in each league—had an ERA between 2.00 and 2.99, so the probability that a pitcher with an ERA between 2.00 and 2.99 was a National League pitcher is 0.5.

The correct answer is (C).
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The graph is a frequency distribution of the earned run averages (ERA) 02 Mar 2025, 11:15
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