Question

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1-56 An airline in a small city has five departures each day. It is known that any given flight has a probability of 0.3 of departing late. For any given day find the probabilities that: (a) no flights depart late, (b) all flights depart late, and (c) three or more depart on time.

Answer 1

Question 1.56) XBinomial(n -5,p 0.3) PlX-0)-(2)pr(1 _ p)"--(o) (0.3)"(1-0.3)5-0-1 * (0.3)"(0.7)" 0.16807 0.168070 0.168 P(X 0) 0.168 Using excel function BinomDist (0,5,0.3,false) or TI-83/84 function binompdf (5,0.3,0), exact answer is 0.16807 X ~ Binomial (n 5,p = 0.3) PlX = 5)-(2)pr(1-p)"-r- 0.00243 0.0024300.002 (5) (0.3)*(1 -0.3 )5-5-1 * (0.3)5(0.7)。 P(x5) 0.002 Using excel function BinomDist (5,5,0.3,false) or TI-83/84 function binompdf (5,0.3,5), exact answer is 0.00243

C P(Y > 3), n-5, p-0.7 = P(Y = 3) + P(Y-4) + P(Y-5) (because these are disjoint events) PY 3 () (0.7)3(1 -0.7)2 10(0.7) (0.3)2 0.3087 P(Y-4)3)(0.7)4(1 -0.75(0.7)(0.3)36015 P(Y = 5)-(2) (0.7)5(1-0.7)" = 1(0.7)5 (0.3)0-0.16807 0.30870.36015 + 0.16807-0.836920 0.837 P(Y 23)-0.837 Using excel function1 - BinomDist(2, 5,0.7, true) or TI-83/84 function 1 - binomcdf (5, 0.7,2), exact answer is 0.83692 ~^Thank you ,ne。 Chegg's tutoring gudelines state that the experts can solve only 1 question in case of multiple questions. Solving too many questions in a single thread sets up unrealistic expectations, leading to poor ratings for tutor in the future Hope you understand, and sorry for the inconvenience. I would be glad to help if there is any doubt regarding my solution above PS: You might need to post the question again, and if you do so, please mention to solve what I missed here.)