homework math question section 6.2

Question

According to​ flightstats.com, American Airlines flights from Dallas to Chicago are on time

80​%

of the time. Suppose

25

flights are randomly​ selected, and the number of​ on-time flights is recorded.

​(a) Explain why this is a binomial experiment.

​(b) Determine the values of n and p.

​(c) Find and interpret the probability that exactly

16

flights are on time.

​(d) Find and interpret the probability that fewer than

16

flights are on time.

​(e) Find and interpret the probability that at least

16

flights are on time.

​(f) Find and interpret the probability that between

14

and

16

​flights, inclusive, are on time.

Answer 1

(a) Binomial distribution can be used if the probability experiment satifies four conditions:

1. Fixed number of independent trails.
2. Only two possible outcomes: success or failure. In this example it's on-time (success) or not on time (failure).
3. Probability of success is same for each trial.
4. The random variable x counts the number of successful trials.

(b) n = 25; p = 0.80

(c) Probability of exactly 16 [P(16)] you can use formula or table (available on line, but need table that goes to N = 25, highly recommended for this problem) Formula is P(x) = [n!/(n - x)!x!]p^xq^n-x. n = 25; p = 0.8; q = 0.2; x = 16. Or you can use the formula with a Combination factor. The table gives a probability of exactly 16 successes as 0.029.

(d) For fewer than 16, have to repeat the above for all values of n = 0 -> 15 and add them. Or, do sum of 16 -> 25 and subtract the result from 1.0.

(e) At least 16 is sum of probabilities of P(16) -> P(25).

(f) Find P(14), P(15) and P(16) and add them.