Question

Exercise 2. The probability that a worker arrives at time to his workplace is 0.95. From a sample of 10 workers, (a) find the probability that only one worker arrives late to his workplace (b) find the probability that at least one worker arrives at time to his workplace. (c) find the probability that at most two workers arrive at time to his workplace. (d) find the average number of workers arriving at time to his workplace.

Answer 1

let probability arrive at time =p so we have p = 0.95 probability arrive late = q = 0.05 given n=10 Poob only one worker arrive late to his work place (a) - PC X=1) = . Co » P(x=1) = loc. (0.05) (0.95)' Jo x 6 x 063 025 = 0.3151 Ans. . (b) Probability at least one worker arrive better at time 1 - PC x = 0) . = 1- nco bºqu-o 1 1060 (0.45° (0.05)) 1 - 9.7656 x 1014 z - Approa (C) peat most two) = P(x=0s + P(x=1) +8(2=2) = 9.7650 xicht loc (0.9colas't loc26.95 (0.05 I 1688S X lo coll Average = m = 10 x 0.95 = 9.5 = lo Approx 10-10 => PC x= 10) = loc. (0.95) (0.05) = 1 x 0.59874 x 1 = 0.59874 Ansi