Question

American Airlines flights from Dallas to Chicago are on-time 80% of the time. Suppose 15 flights are randomly selected, and the number of on-time flights is recorded. Find and the probability that exactly 10 flights are on time.

Answer 1

about 8 flights

Explanation:

Answer 2

Probability that exactly 10 flights are on time is 0.1032.

Explanation:

We are given that American Airlines flights from Dallas to Chicago are on-time 80% of the time. Suppose 15 flights are randomly selected, and the number of on-time flights is recorded.

The above situation can be represented through Binomial distribution;

`P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....`

where, n = number of trials (samples) taken = 15 flights

r = number of success

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

are on time, i.e., 80%

LET X = Number of flights that are on time

Also, it is given that a sample of 15 flights is taken,

So, it means X ~
`Binom(n=15, p=0.80)`

So, Probability that exactly 10 flights are on time = P(X = 10)

P(X = 10) =
`\binom{15}{10}0.80^(10) (1-0.80)^(15-10)`

=
`3003 * 0.80^(10) * 0.20^(5)`

= 0.1032

Therefore, Probability that exactly 10 flights are on time is 0.1032.