The frequency of color blindness in the Caucasian American male population is about 8%. If a random sample of 125 individuals is chosen from this population, what is the probability that 5-10 individuals in the sample are color blind?
To calculate the probability that 5-10 individuals in the sample are color blind, we can use the binomial probability formula. The formula is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
where:
P(X=k) represents the probability of having exactly k successes (in this case, individuals who are color blind),
C(n, k) is the number of ways to choose k successes out of n individuals (binomial coefficient),
p is the probability of a success (probability of being color blind), and
n is the total number of trials (sample size).
In this case, n = 125 (sample size) and p = 0.08 (probability of being color blind).
Now, let's calculate the probability that 5-10 individuals are color blind:
P(5 ≤ X ≤ 10) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)
= C(125,5) * (0.08)^5 * (1-0.08)^(125-5)
+ C(125,6) * (0.08)^6 * (1-0.08)^(125-6)
+ C(125,7) * (0.08)^7 * (1-0.08)^(125-7)
+ C(125,8) * (0.08)^8 * (1-0.08)^(125-8)
+ C(125,9) * (0.08)^9 * (1-0.08)^(125-9)
+ C(125,10) * (0.08)^10 * (1-0.08)^(125-10)
Now, we can calculate each term using a calculator or statistical software. Add up all the probabilities to get the final answer.
Note: The binomial probability formula assumes independent and identical trials. In this case, it assumes each individual's color blindness status is independent of others, and the probability of color blindness remains the same for all individuals.