ts on a certa in route are on time 85% of the time. Suppose 25 flights are rando
ID: 3049618 • Letter: T
Question
ts on a certa in route are on time 85% of the time. Suppose 25 flights are randomly selected and the number of on-time flights is record According to an airline, fligh (a) Explain why this is a binomial experiment d and interpret the probability that exactly 18 flights are on time (c) Find and interpret the probability that fewer than 18 flights are on time (d) Find and interpret the probability that at least 18 flights are on time (e) Find and interpret the probability that between 16 and 18 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. There are two mutually exclusive outcomes, success or failure C. The probability of success is the same for each trial of the experiment. D. The experiment is performed a fixed number of times. E. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late The experiment is performed until a desired number of successes is reached G. Each trial depends on the previous trial F. Click to select your answer(s) and then click Check Answe partsExplanation / Answer
p = 0.85
n = 25
a) Option-A, B, C, D
b) P(X = 18) = 25C18 * 0.8518 * 0.157 = 0.0441
c) P(X < 18) = 1 - P(X > 18)
= 1 - (P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25))
= 1 - (25C18 * 0.8518 * 0.157 + 25C19 * 0.8519 * 0.156 + 25C20 * 0.8520 * 0.155 + 25C21 * 0.8521 * 0.154 + 25C22 * 0.8522 * 0.153 + 25C23 * 0.8523 * 0.152 + 25C24 * 0.8524 * 0.151 + 25C25 * 0.8525 * 0.150 )
= 1 - (0.9745)
= 0.0255
d) P(X > 18) = 1 - P(X < 18) = 1 - 0.0255 = 0.9745
e) P(16 < X < 18) = P(X = 16) + P(X = 17) + P(X = 18)
= 25C16 * 0.8516 * 0.159 + 25C17 * 0.8517 * 0.158 + 25C18 * 0.8518 * 0.157
= 0.0674
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