Based on the 2009 season, the Texas Rangers have a winning percentage of .533. Use the binomial model to find the probability that the Rangers win 4 of their next 5 games.
P(x) = [n!/ x!(n-x)!] P^xQ^n-x
a. 12.4%
b. 18.8%
c. 23.7%
d. 50%
To use the binomial model to find the probability, we need to determine the values for n, x, P, and Q.
In this case, n is the number of trials (games), which is 5.
x is the number of successful trials (games won), which is 4.
P is the probability of success in each trial (winning percentage), which is 0.533.
Q is the probability of failure in each trial (losing percentage), which is 1 - P = 1 - 0.533 = 0.467.
Now, we can plug these values into the binomial model formula:
P(x) = [n!/ x!(n-x)!] * P^x * Q^(n-x)
P(4) = [5!/ 4!(5-4)!] * 0.533^4 * 0.467^(5-4)
Simplifying the equation:
P(4) = (5/1) * 0.533^4 * 0.467^1
P(4) = 5 * 0.533^4 * 0.467
P(4) = 5 * 0.10879 * 0.467
P(4) = 0.2546
Converting this to a percentage, the probability that the Rangers win 4 of their next 5 games is 25.46%.
Therefore, the correct option is not listed among the answer choices.