Earned run average A baseball pitcher’s earned run average (ERA) is A(e, i) = 9e/i, where e is the number of earned runs given up by the pitcher and i is the number of innings pitched. Good pitchers have low ERAs. Assume e ≥ 0 and i > 0 are real numbers.a. The single-season major league record for the lowest ERA was set by Dutch Leonard of the Detroit Tigers in 1914. During that season, Dutch pitched a total of 224 innings and gave up just 24 earned runs. What was his ERA?b. Determine the ERA of a relief pitcher who gives up 4 earned runs in one-third of an inning.c. Graph the level curve A(e, i) = 3 and describe the relationship between e and i in this case.
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.
Earned run average A baseball pitcher’s earned run average (ERA) is A(e, i) = 9e/i, where e is the number of earned runs given up by the pitcher and i is the number of innings pitched. Good pitchers have low ERAs. Assume e ≥ 0 and i > 0 are real numbers.
a. The single-season major league record for the lowest ERA was set by Dutch Leonard of the Detroit Tigers in 1914. During that season, Dutch pitched a total of 224 innings and gave up just 24 earned runs. What was his ERA?
b. Determine the ERA of a relief pitcher who gives up 4 earned runs in one-third of an inning.
c. Graph the level curve A(e, i) = 3 and describe the relationship between e and i in this case.
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