Description
Problem: BASEBALL: The number of games played in the World Series from 1903 to 2009.
Games Played 4 5 6 7 8
Frequency 20 23 23 36 3
(a) Use the frequency distribution to construct a probability distribution.
(b) Graph the probability distribution using a histogram and describe its shape.
(c) Find the mean, variance, and standard deviation of the probability distribution.
(d) Interpret the results in the context of the real life situation.
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Explanation & Answer
Frequency Distribution
| x | p(x) | xp | x^2*p | |
| 4 | 20/105 | 80/105 | 320/105 | |
| 5 | 23/105 | 115/105 | 575/105 | |
| 6 | 23/105 | 138/105 | 828/105 | |
| 7 | 36/105 | 252/105 | 1764/105 | |
| 8 | 3/105 | 24/105 | 192/105 | |
| ∑xp = 609/105 = 5.8 | ∑x^2p=3679/105=35.03 | |||
Variance = 35.03 - (5.8)^2 = 35.03 - 33.64 = 1.39
S.D = square root of 1.39 = 1.17
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