Final answer:
To calculate the probability of exactly 97 out of 100 runners finishing the marathon, use the binomial probability formula. The probability is approximately 9.9%.
Step-by-step explanation:
To calculate the probability that exactly 97 out of 100 runners finished the marathon, we need to use the binomial probability formula. The formula is:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
Where P(x) is the probability of x successes, n is the total number of trials, p is the probability of success in each trial, and C(n, x) is the combination of n items taken x at a time.
In this case, n = 100, x = 97, p = 0.974, and 1-p = 0.026.
Plugging the values into the formula, we get:
P(97) = C(100, 97) * (0.974)^97 * (0.026)^(100-97)
Calculating the combination and the probabilities, we find the probability that exactly 97 of the 100 runners finished the marathon is approximately 0.099 or 9.9%.