Interpret Probability

Question

According to a certain airline, flights on a certain route are on time 85% of the time. Suppose 17 flights are randomly selected and the number of on-time flights is recorded.

Find and interpret the probablity that ezactly 12 flights are on time?

" " " Fewer than 12 are on-time?

" " " At least 12 flights are on-time?

" " " Between 10 and 12 flights are on-time inclusive ?

Answer 1

use binomial distribution formula for p = 0.85, n = 17, x = number of successes (flights on time)

P(x = k) = n ! p^k * (1-p) ^ n-k

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k! (n-k)!

P(x = 12) = 0.0668

P(x < 12) = 0.0319

P(x >= 12) = 0.9681

P(10 <= x <= 12) = P(x = 10) + P(x = 11) + P(x = 12) = 0.0065 + 0.0236 + 0.0668