Question

1. Rates of on-time flights for commercial jets are continuously tracked by the U.S Department of Transportation. Recently, Southwest Air had the best rate with 80% of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. Find the probability that exactly 10 flights arrive on time.

(a) .206        (b) .103        (c) .010         (d) .188        (e) .003

2. Refer to question 11. Find the probability that at least 10 flights arrive on time.

(a) .939        (b) .061        (c) .854        (d) .759        (e) .093 show using a TI-84

Answer 1

p = 0.8

n = 15

This is a binomial distribution.

P(X = x) = 15Cx * 0.8^x * (1 - 0.8)^15-x

a) P(X = 10) = 15C10 * 0.8¹⁰ * 0.2⁵ = 0.103

Option-B) 0.103

b) P(X > 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

                    = 15C10 * 0.8¹⁰ * 0.2⁵ + 15C11 * 0.8¹¹ * 0.2⁴ + 15C12 * 0.8¹² * 0.2³ + 15C13 * 0.8¹³ * 0.2² + 15C14 * 0.8¹⁴ * 0.2¹ + 15C15 * 0.8¹⁵ * 0.2⁰

                    = 0.939

Option-A) 0.939