Question

At a certain airport, 80% of the flights arrive on time. A sample of 14 flights is studied. 1) Find the probability that 9 flights were on time 2) Find the probability that exactly 10 of the flights were on time 3) Find the probability that 11 or more of the flights were on time Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.

Answer 1

Let X be number of flights on time.

X follows Binomial distribution with parameters; sample size = n = 14 and probability of flights arrive in time = P = 0.8

Hence,

P(X=x) = ⁿC_x * P^x *(1-P)^(n-x)

1.

Probability that 9 flights were on time

P(X = 9) = ¹⁴C₉ * 0.8^9 * (1-0.8)^(14-9)

P(X = 9) = 0.0860

2.

Probability that 10 flights were on time

P(X = 10) = ¹⁴C10 * 0.8^10 * (1-0.8)^(14-10)

P(X = 10) = 0.1720

3.

Probability that 11 or more flights were on time

= P(X>=11)

= P(X=11) + P(X=12) + P(X=13) + P(X=14)

= ¹⁴C11 * 0.8^11 * (1-0.8)^(14-11)

+ ¹⁴C12 * 0.8^12* (1-0.8)^(14-12)

+ ¹⁴C13 * 0.8^13 * (1-0.8)^(14-13)

+ ¹⁴C14 * 0.8^14 * (1-0.8)^(14-14)

= 0.6982