Final answer:
The binomial probabilities can be computed using the binomial distribution formula, substituting the values for n, x, and p accordingly, and summing individual probabilities for ranges of successes.
Step-by-step explanation:
The binomial probabilities in question can be computed directly using the binomial distribution formula b(x; n, p), which is defined for a fixed number of independent trials (n), a constant probability of success in each trial (p), and a specific number of successes (x). The formula to compute this is: P(X = x) = (n choose x) p^x (1-p)^(n-x). For each part: b(5; 8, 0.35) - Using the formula, you should substitute n = 8, x = 5, and p = 0.35 to calculate the probability. b(6; 8, 0.6) - Here you substitute n = 8, x = 6, and p = 0.6. P(3 ≤ X ≤ 5) when n = 7 and p = 0.55 - You calculate the probability for X = 3, 4, and 5 individually and then sum them to get the total probability. P(1 ≤ X) when n = 9 and p = 0.1 - To find this cumulative probability, you would need to compute the probabilities for X = 1 up to X = 9 and sum them. Each part requires individual computations, and the results should be rounded to three decimal places.