The rates of on-time flights for commercial jets are continuously tracked by the U. S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 13 flights arrive late .

The probability that at least 13 flights arrive late is 2.5196 .

Step-by-step explanation:

We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.

A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.

The above situation can be represented through binomial distribution;

where, n = number of trials (samples) taken = 18 Southwest flights

           r = number of success = at least 13 flights arrive late

          p = probability of success which in our question is probability that

                flights arrive late, i.e. p = 1 - 0.80 = 20%

Let X = Number of flights that arrive late.

So, X ~ Binom(n = 18, p = 0.20)

Now, the probability that at least 13 flights arrive late is given by = P(X 13)

P(X 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)

=

=

= 2.5196 .

answer: 43/157

this is the answer and if you try to prove me wrong your a meanie