Below are Earned Run Averages for the indicated Leagues. LKAGUK Mean of Earned Run Averages of Starting 2016 AL 2022 A.L 2076 N.L 2.99 4.95 5.29 Pitchers Standard Devintion of Earned Run .59 .56 .76 Averages of Starting Pitchers | Sebastian: 1.08 |Caruthers: 1.34 Mungo: 1.81 Assume that all distributions are normal. Note: the lower an Earned Run Average is, the better (more impressive) it is. (a) Rank Sebastian, Caruthers, and Mungo in impressiveness relative to their respective Leagues. (b) What would Mungo's Earned Run Average have to have been in 2078 for his performance to have been exactly as impressive as was Caruthers' in 2022? (c) What would a pitcher's Earned Run Average have to have been in 2022 to have been in the lowest 3% of Earned Run Averages?

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Below are Earned Run Averages for the indicated Leagues.
LEAGUK
Mean of Earned Run
Averages of Starting
Pitchers
Standard Deviation
of Earned Run
Averages of Starting
Pitchers
2016 AL.
2022 AL
2078 N.L.
2.99
4.95
5.29
.59
.56
.76
Sebastian: 1.08
| Caruthers: 1.34
1.81
Mungo:
Assume that all distributions are normal.
Note: the lower an Earned Run Average is, the better (more impressive) it is.
(a) Rank Sebastian, Caruthers, and Mungo in impressiveness relative to their respective Leagues.
(b) What would Mungo's Earned Run Average have to have been in 2078 for his performance to
have been exactly as impressive as was Caruthers' in 2022?
in the
(c) What would a pitcher's Earned Run Average have to have been in 2022 to have
lowest 3% of Earned Run Averages?
Transcribed Image Text:Below are Earned Run Averages for the indicated Leagues. LEAGUK Mean of Earned Run Averages of Starting Pitchers Standard Deviation of Earned Run Averages of Starting Pitchers 2016 AL. 2022 AL 2078 N.L. 2.99 4.95 5.29 .59 .56 .76 Sebastian: 1.08 | Caruthers: 1.34 1.81 Mungo: Assume that all distributions are normal. Note: the lower an Earned Run Average is, the better (more impressive) it is. (a) Rank Sebastian, Caruthers, and Mungo in impressiveness relative to their respective Leagues. (b) What would Mungo's Earned Run Average have to have been in 2078 for his performance to have been exactly as impressive as was Caruthers' in 2022? in the (c) What would a pitcher's Earned Run Average have to have been in 2022 to have lowest 3% of Earned Run Averages?
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