w5. On-Time Flights According to flightstats.com, American Airlines flights from

Question

w5. On-Time Flights According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 15 flights are randomly selected, and the number of on-time flights is recorded. a) Explain why this is a binomial experiment. (b) F ind and interpret the probability that exactly 10 flights are on time. ind and interpret the probability that fewer than 10 flights are on time. ) F nd and interpret the probability that at least 10 flights are on time. e) Find and lights id interpret the probability that between 8 and 10 ghts, inclusive, are on time. lun Organization found

Explanation / Answer

a) According to the binomial conditions, we have

=> 15 independent and finite flights

=> The fights which are on time is taken as success, other wise is failure. So here we have two disjoint outcomes

b) Using pmf of binomial distribution

p [x = 10] = 15c10 * 0.810 * 0.25

= 0.1032

  This event occurs with only 10.32% chance

c) p [x < 10] = 1 - p [10] + p [11] + p [12] + p [13] + p [14] + p [15]

= 0.0611

It has only 6.11%

d) p [x >= 10] = p [10] + p [11] + p [12] + p [13] + p [14] + p [15] = 0.9389

this event is more likely,

e) p [8 < x < 10] = p[9] = 10c9 * 0.89 * 0.26 = 0.0430

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