(31) A baseball teams plays 182 games in a season and we are tracking their record over three seasons. Assume the probability the team wins each game in Season 1, Season 2, and Season 3 is 0.45, 0.6, and 0.4, respectively. Let X be the total number of games the team wins over the three seasons. (a) Use Poisson approximations to binomial distributions to estimate P(X = 260). (b) Use normal approximations to binomial distributions to estimate P(X > 270).
(31) A baseball teams plays 182 games in a season and we are tracking their record over three seasons. Assume the probability the team wins each game in Season 1, Season 2, and Season 3 is 0.45, 0.6, and 0.4, respectively. Let X be the total number of games the team wins over the three seasons. (a) Use Poisson approximations to binomial distributions to estimate P(X = 260). (b) Use normal approximations to binomial distributions to estimate P(X > 270).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![(31) A baseball teams plays 182 games in a season and we are tracking their record over three
seasons. Assume the probability the team wins each game in Season 1, Season 2, and
Season 3 is 0.45, 0.6, and 0.4, respectively. Let X be the total number of games the team
wins over the three seasons.
(a) Use Poisson approximations to binomial distributions to estimate P(X = 260).
(b) Use normal approximations to binomial distributions to estimate P(X > 270).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5434c8-3dcd-4d86-911b-2b3deb814891%2F952c8cdc-20ca-4265-afd8-37e4deb3dccf%2Fp5nsfj4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(31) A baseball teams plays 182 games in a season and we are tracking their record over three
seasons. Assume the probability the team wins each game in Season 1, Season 2, and
Season 3 is 0.45, 0.6, and 0.4, respectively. Let X be the total number of games the team
wins over the three seasons.
(a) Use Poisson approximations to binomial distributions to estimate P(X = 260).
(b) Use normal approximations to binomial distributions to estimate P(X > 270).
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