Question

HW4 Binomial Random Variables: Problem 2 Previous Problem Problem List Next Problem (1 pont) BlueSky Air has the best on-time arrival rate with 80% ot its nights arriving on time A test is conducted by randomly selecting 16 Bluesky Air flights and observing whether they arrive on time What is the probability that 2 fights of BlueSky Air arrive late? (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places) Probability (as a proportion)

Answer 1

BlueSky Air has the best on-time arrival rate of 80% of flights arriving on time.

P(a flight arrives on time) = 0.8, P(a flight arrives late) = 1 - 0.8 = 0.2;

p= 0.2 i.e. the probability that a flight arrives late is 0.2

Let X denote the number of flights of BlueSky Air which arrive late.

A test is conducted by randomly selecting 16 BlueSky Air flights.

There are two possibilities, either the flight is on time or it is late. If we consider the event that the flight is late, as success then, X ~ Bin(16, 0.2)

P( 2 flights of BlueSky Air arrives late ) = P [ X = 2 ] = ¹⁶C₂ * (0.2)² * (0.8)^16-2 = 0.2111062 = 0.211 (approximately)