Question

Chapter 5: Problem Set 10 Calenlate the following binomial probabilities by either using one of the binomial probahility tables, or calculating the probability with a calculator or software using the formmla n Piain,p) ald where g-1-P (a) Pr-4,n-15,p2) (b) P(z-9,n-12,p 75) (e) P(r>6,n-10, p 8) (d) P(z<20, n-20,p- 9) 11. Cards: Suppose you draw a card from a deck (with replacement) 10 times in a row What is the probability that you get exactly 4 hearts? 0- 12. Lie Détector: Suppose a lie detector allows 20 % of all lies to go undetected. If you take the test snd tell 10 lies, would 5 undetected lies be an unmusually large number of undetected lies? Use the criteria that a number (r) is unusually large if P(r or more) < 0.05 13. T/F Quiz: Suppose you take a 10 question True or False quiz and you guess on every problem You only get 2 correct. Is this an unusually low number of correct guesses. Use the criteria that a number (z) is unusually low if P(r or less) 0.05. 14. Over-booking Flights: At Low Budget Air (LBA), historical data shows that 95% of all passengens show up in time to board. Therefore, they occasionally over-book flights in hopes of filling each plane to capacity. Here we consider some probabilities associated with this type of issue. Suppose a small plane has a capacity of 20 passengers. They book 20 passengers for a flight on this plane (a) What is the probability that exactly 20 passengers show up (b) What is the probability that exactly 19 passengers show up? (c) What is the probability that they will have at least one empty seat? (d) If only 17 passengers shou up, would that be considered an unusually low number of passenge Use the criteria that a number (z) is unusually low if P(z or less) S 0.05 (e) If only 16 passengers show up, would that be considered an unusually low uumber of paseng Use the criteria that a number (x) is unusually low if P(z or less) S 0.05

Answer 1

x nx ni P pé ot Z que ,q=1-P - P(x/n, ) - _ - (1-x) 6 KI (a) P(x=4, n=15, p=0.2) 9=1-P=10.2=0.8 15! (0-27%E0%) 5.4 (15-4)141 = 15! (02)*(03) = 0.1876 11! 4! 2:10.75= 0.25 2:1-075=0.25 (B) P (2=9, n=12, P=0.75) 1. 121 (6.75 (0.252-9 (12-9)19? 3191 o.8 = 12? (075)" (0:25)= 0-2581 (C) PCX76, 1-10,P=0.8) 221-0-870-2 *76=> x=7, 8, 90210 - P(x=7,0=10, p=08) + P(x=8,0210, p=08) + P(x=9, 1-10,8208) + P(X=10,:10, P78) - 101(0.8) (0.2²+ 10! (0.5) (0.2)? 3171 218? + 10! (03806027° + 10! (05) 2023 - 0879/ 1! 91 0! 10!

/۵۰ =7 = 2 (27 - 20 - ا, مے لا ) (of) = (a7 عرفه =H مد= P ( x :مروح) 5 /۸۵ ان = - ( ماه 87 -