Final answer:
The probability that five or fewer people will have the eye disease in a random sample of 25 people is approximately 0.9020.
Step-by-step explanation:
To find the probability that five or fewer people will have the eye disease in a random sample of 25 people, we can use the binomial distribution. The formula for the binomial distribution is P(X ≤ k) = ∑(from x=0 to k) of (nCx * p^x * q^(n-x)), where n is the number of trials, p is the probability of success, q is the probability of failure (1-p), and k is the number of successes we are interested in.
In this case, n=25, p=0.10, and q=0.90. We want to find P(X ≤ 5), so k=5. Plugging these values into the formula, we get P(X ≤ 5) = ∑(from x=0 to 5) of (25Cx * (0.10)^x * (0.90)^(25-x)).
Using the binomial table or a calculator, we find that P(X ≤ 5) is approximately 0.9020.