Question

1.United Airlines' flights from Chicago to Atlanta are on time 60 % of the time. Suppose 7 flights are randomly selected, and the number on-time flights is recorded.
Round answers to 3 significant figures.

The probability that exactly 6 flights are on time is =

The probability that at most 3 flights are on time is =

The probability that at least 5 flights are on time is

Answer 1

Here, n = 7, p = 0.6, (1 - p) = 0.4 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 6)
P(X = 6) = 7C6 * 0.6^6 * 0.4^1
P(X = 6) = 0.131

b)

Here, n = 7, p = 0.6, (1 - p) = 0.4 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 3).
P(X <= 3) = (7C0 * 0.6^0 * 0.4^7) + (7C1 * 0.6^1 * 0.4^6) + (7C2 * 0.6^2 * 0.4^5) + (7C3 * 0.6^3 * 0.4^4)
P(X <= 3) = 0.002 + 0.017 + 0.077 + 0.194
P(X <= 3) = 0.290

c)

Here, n = 7, p = 0.6, (1 - p) = 0.4 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 5).
P(X >= 5) = (7C5 * 0.6^5 * 0.4^2) + (7C6 * 0.6^6 * 0.4^1) + (7C7 * 0.6^7 * 0.4^0)
P(X >= 5) = 0.261 + 0.131 + 0.028
P(X >= 5) = 0.420