Question

5 DISCRETE PROBABILITY DISTRIBUTIONS (21) The number of aircraft landing at London Heathrow Airport per day is an example of a discrete random variable. (1) True. (2) False. (22) Which of the following is not a characteristic of a binomial experiment? (1) The experiment consists of n identical trials. (2) The trials are independent. (3) Each trial results in one of two outcomes (commonly referred to as success, S, and failure, F). (4) The probability of success, p, should be close to 0.5. Problem E: The data generated by a credit card company indicates that 40% of its clients pay their bills late. Suppose 20 clients of this company are selected at random. (23) Refer to Problem E. How many of them would you expect to pay their bill late? (3) 6 (4) 10 (2) 8 (24) Refer to Problem E. What is the probability that exactly 5 of them pay their bill late? (1) 0.126 (3) 0.075 (2) 0.051 (4) 0.177 (25) Refer to Problem E. What is the probability that more than 10 pay their bill late? (1) 0.913 (2) 0.245 (3) 0.057 (4) 0.128

Answer 1

a 21) The number of aircraft landing at London Heathrow Airport per day is on example of discrete random variable Ans: ® True ng at all, since they are A random variable von is called discrete if it has either a finite on a countable no. of possible values. Here, no. of aircraft landings are likes 11, 2,4 a 22) which of the following is not characteristic of a binomial experiment. © Ans @ the probability of suuess ip, should be close to o.5. since, All of the other options in aress the chara- cteristic of a binomial experiment. no. of pooblem E] afoo (ang let be the number of clients pay their bills late 200 loeng Here, probability of suuress, p=014 (4007) ie, probability Clients pay their bills flate id as and pro bability of foulure, 951P2 OG 100) i.e. clients, their bills late. probability of no. of does not ro. OF trials, n= 20 Here, XN B (0=20, p = 0:4) know that, if XN BloIP) then its pmF is given by Papay we no a P(x:x) = (a 9 ;a=011, ag... 0 where, 03231; P+9 = 1. cs

nicht now, here XN B (n=20, p=0.4 then its pmf is given by and E(X)= np. 2012 s 23 pay plx-x) = level) (0.4) Cour) 12:03 1,23 -- 20 Here, we have to find the expected no of clients their bilt late towali je ? E(X) - np. Here, n320 i PE 0.4 ..; ECX) - 20 x04 - 8 Ans: 12 8 p&actly sos 24) Here, we have to find the probability them pay their bill late afte odt le P(x=5) = 1500 20-5 ) (0.4)(0.6) P(x=5 5 0.075 . Ans: 13 0.075 1:25) We have to find the probability than more than to pay their bill pate le P(x210) = P(X=11) + P(X=12) + +P(x=20) to P(x710 )it 091281311 ༢་་༢་ ལན .: Ans" (4 0.128 CS