According to an airline, flights on a certain route are on time 80% of the time.
ID: 3064579 • Letter: A
Question
According to an airline, flights on a certain route are on time 80% of the time. Suppose 10 flights are randomly selected and the number of on-time flights is recorded (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 6 flights are on time (c) Find and interpret the probability that fewer than 6 flights are on time (d) Find and interpret the probability that at least 6 flights are on time (e) Find and interpret the probability that between 4 and 6 flights, inclusive, are on time (a) Identify the statements that explain why this is a binomial experiment. Select all that apply A. The trials are independent. B. The experiment is performed until a desired number of successes is reached C. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late D. The probability of success is the same for each trial of the experiment. E. Each trial depends on the previous trial F. There are two mutually exclusive outcomes, success or failure G. The experiment is performed a fixed number of times (b) The probability that exactly 6 flights are on time is (Round to four decimal places as needed.) Interpret the probability In 100 trials of this experiment, it is expected aboutto result in exactly 6 flights being on time (Round to the nearest whole number as needed.) (c) The probability that fewer than 6 flights are on time is (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected about to result in fewer than 6 flights being on time (Round to the nearest whole number as needed.) (d) The probability that at least 6 flights are on time is (Round to four decimal places as needed.) Interpret the probability In 100 trials of this experiment, it is expected about LI to result in at least 6 flights being on time (Round to the nearest whole number as needed.) (e) The probability that between 4 and 6 flights, inclusive, are on time is (Round to four decimal places as needed.) Interpret the probability In 100 trials of this experiment, it is expected aboutto result in between 4 and 6 flights, inclusive, being on time (Round to the nearest whole number as needed.)Explanation / Answer
(a) (A) The trials are independent. Option is true
(B) Option B is wrong.
(C) Option C is also wrong
(D) Option D is correct as Pr(Success) is same for each even
(E) Option E is correct.
(F) Here Option F is also correct
(G Option G is also correct.
(b) Here n = 10 and p = 0.80
Pr(x = 6) = BIN (x = 6 ; 10 ; 0.80) = 0.0881
In 100 trials of experiment, it is about 9 to result in fewer than 6 flights being on time.
(c)
Here n = 10 and p = 0.80
Pr(x < 6) = BIN (x < 6 ; 10 ; 0.80) = 0.0328
In 100 trials of experiment, it is about 3 to result in fewer than 6 flights being on time.
(d) Pr(x 6) = 1 - Pr(x < 6) = 1 - 0.0328 = 0.9672
in 100 trials, it is expected about 97 to result in at least 6 flights being on time.
(e) Pr(4 x 6) = BIN (X = 4 ,5,6 ; 10 ; 0.8) = 0.1200
In 100 rials of experiment, it is expected about 12 to result in between 4 and 6 flights, inclusive, being on time.
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