Question

United Airlines flights from Boston to Seattle are on time 70 % of the time. Suppose 13 flights are randomly

selected, and the number on-time flights is recorded.
1. The probability that at least 6 flights are on time is
2. The probability that at most 6 flights are on time is
3. The probability that exactly 9 flights are on time is

Answer 1

1. The probability of at least 6 flights being on time can be calculated as the sum of the probabilities of 6, 7, 8, 9, 10, 11, 12 and 13 on-time flights:
I hope this helped you (:
2. The probability that at most 6 flights are on time can be calculated as the sum of the probabilities of 0, 1, 2,

Explanation:

We can use the binomial probability formula to solve this problem.

Let's denote:

- n = 13 (number of flights)

- p = 0.70 (probability of punctual flights)

1. The probability of at least 6 flights being on time can be calculated as the sum of the probabilities of 6, 7, 8, 9, 10, 11, 12 and 13 on-time flights:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9 ) + P(X = 10) + P(X = 11) + P (X = 12) + P(X = 13) We can

calculate these individual probabilities using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(nk)

where (n choose k) = n! / (k! * (nk)!)

Let's calculate these probabilities.

2. The probability that at most 6 flights are on time can be calculated as the sum of the probabilities of 0, 1, 2,