A bus company has records showing that its buses arrive on time 95% of the time. Suppose the company operates 65 bus trips each day. The Manager has asked for the probability that 60 or more of these buses arrive on time. Use the binomial distribution to determine the probability that 60 or more buses arrive on time.

To determine the probability that 60 or more buses arrive on time, we can use the binomial distribution. The binomial distribution is a probability distribution that calculates the probability of a certain number of successes (bus arrivals on time) in a fixed number of independent trials (bus trips).

Let's break down the problem using the following information:
- The probability of a bus arriving on time is 0.95 (95%).
- The company operates 65 bus trips each day.

To solve this problem using the binomial distribution, we need to calculate the cumulative probability of 60 or more successes (bus arrivals on time) out of 65 trials (bus trips).

We can use statistical software or an online calculator to compute this probability. Here's how to do it manually using the binomial formula:

1. Calculate the probability of exactly k successes (60, 61, 62, ... 65) using the formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where n is the number of trials, k is the number of successes, p is the probability of success.

2. Sum up the probabilities for k = 60 to 65:
P(X >= 60) = P(X = 60) + P(X = 61) + ... + P(X = 65)

This manual calculation involves multiple calculations, so it might be easier to use a calculator or software that handles binomial distribution calculations.

Using statistical software or an online calculator, entering the values of n = 65, p = 0.95, and calculating the cumulative probability P(X >= 60), we can find the probability that 60 or more buses arrive on time. The result will be the probability you asked for.

Remember, the binomial distribution calculates the probability of a specific number of successes in a fixed number of trials, given a probability of success.