Question

In the 2019 Boston Marathon, approximately 97.4% of all runners who started the race were able to complete the 42.2 km (26.2 mile) course. If 100 runners are chosen at random, what is the probability that exactly 97 of them finished the marathon?

Answer 1

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%.