Question

Your flight has been delayed: At Denver International Airport, 84% of recent flights have arrived on time. A sample of 12 flights is studied. Round the probabilities to four decimal places. Part 1 of 4 (a) Find the probability that all 12 of the flights were on time. The probability that all 12 of the flights were on time is Part 2 of 4 (b) Find the probability that exactly 10 of the flights were on time. The probability that exactly 10 of the flights were on time is Part 3 of 4 (c) Find the probability that 10 or more of the flights were on time. The probability that 10 or more of the flights were on time is Part 4 of 4 (d) Would it be unusual for 11 or more of the flights to be on time? It (Choose one) be unusual for 11 or more of the flights to be on time since the probability is 囗 would would not

Answer 1

85 % of recent flights have arrived on time Therefore probability of recent flights have arrived on time p = 84/100 number of sample n = 12 Let x be the number of flights have arrived on time Therefore x be a binomial (n, p) = (12, 84/100) variable Therefore probability density function of X p(x = i) = (n i) p^i (1 - p)^n - i (a) The probability that all 12 of the flights were m time is p (x = 12) = (12 12) . (84/100)^12 (1 - 84/100)^12 - 12 = (84/100)^12 = 0.1234 (Round of to four decimal places) (b) The probability that exact 10 of the flights where on time is P (x = 10) = (12 10). (84/100)^10. (1 - 84/100)^12 - 10 = 66 times (84/100)^10 times (16/100)^2 = 0.2955 (Round of to four decimal places) (c) The probability that 10 on more of the flights were on time is P (x = 10) + p