Brianna M.

asked • 08/15/17

MATH QUESTION!! NEED HELP

After 75 games of the 2009 baseball season, the Texas Rangers had a record of 40 wins and 35 losses for a winning percentage of .533. You realize that this data fits a binomial model and want to use the formula P(x) = {n! / [x! (n-x)!]} * p^x * q^(n-x) to determine the probability of how many games they will win. How many of the next 15 games should you expect the Rangers to win?
A. 0.467
B. 0.533
C. 7
D. 8

Nolan H.

Walter's answer is right. It's simpler than you are making it. The binomial formula that you brought up in the question tells us the probability of winning a specific number of games. For instance, to find the probability of the Rangers winning EXACTLY 2 games, you would plug in 15 for n, 2 for x, 0.533 for p, and 0.477 for q.
 
If you were to go through this process for each value from 0 to 15, then you would find that the highest probability is for 8 wins. This is unnecessary, though, because the expected win total is just the winning percentage times total games to be played.
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08/15/17

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Walter B. answered • 08/15/17

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This question asks us to find how man games the Rangers expect to win. Expectation is the same as the mean or average.
 
The expected value of an Binomial Variable = p * N where p =  .533 and N = 15.
 
Therefore the expected value = 7.995 or 8.
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