Question

According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are delayed?

Answer 1

Answer:

The probability that all the five flights are delayed is 0.2073.

Step-by-step explanation:

Let X = number of domestic flights delayed at JFK airport.

The probability of a domestic flight being delayed at the JFK airport is, P (X) = p = 0.27.

A random sample of n = 5 flights are selected at JFK airport.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={5\choose x}0.27^{x}(1-0.27)^{5-x};\ x=0,1,2...$

Compute the probability that all the five flights are delayed as follows:

$P(X=5)={5\choose 5}0.27^{5}(1-0.27)^{5-5}=1\times 1\times 0.207307=0.2073$

Thus, the probability that all the five flights are delayed is 0.2073.