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

Answer:

about 8 flights

Step-by-step explanation:

Answer 2

Answer:

Probability that exactly 10 flights are on time is 0.1032.

Step-by-step 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) = $\binom{15}{10}0.80^{10} (1-0.80)^{15-10}$

              = $3003 \times 0.80^{10} \times 0.20^{5}$

              = 0.1032

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