Answer:
To calculate the probability, we can use the binomial probability formula. Let \( p \) be the probability of success (being over age 65), \( n \) be the number of trials (sample size), and \( x \) be the number of successes (patients over age 65).
The formula is:
\[ P(X < 9) = \sum_{x=0}^{8} \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x} \]
Given that \( p = 0.85 \), \( n = 17 \), and \( x < 9 \), you can substitute these values into the formula and calculate the probability. Remember to round the answer to four decimal places.
