Question

O According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you on a bench in a mall and observe people's habits they see What is the probability that among 16 randomly observed individuals actly do not cover their mouth when seering? th) What is the probability that among 16 randomly observed individuals lower than 4 do not cover their mouth when sneezing? c) Would you be surprised the observing 16 individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly individuals do not cover their mouth is Round to four decimal places as needed) (b) The probability that fewer than a individuals do not cover the mouth is (Round to four decimal places as needed) (c) Fower than half of 16 individ covering their mouth be surprising because the probability of observing tower than hall covering thermout when sneering which unusual event Round to four decimal places as needed) Enter your answer in each of the answer boxes S 4 % 5 & 7 2 3 6 8 9 0 Q W E R Т. Y U a Р А. s D F H J к

Answer 1

Probability of wat covering mouth while (P) = 0.267 bailus (sample size) P(x= x) n=16 Xn p(x24) = P(x=0) + P(x=1) + P(x=2) + P(X= 3) sneering is (success) q= I-P - 0.733 Binom P = 0.267) nc. p* q nuk P(x - 5) = 16 P(x=5) 16! 5!!!! P(x=5) 0.19 453 Probabilety that exactly s individual will mouth P(x24) quote a *C3 (0.26735 (0.733) (0-$ (0.267) 5 (0.733)" - مه Nat cover is 0.1945 3 n 도 pe 3 Plx24) = Ž 16c, (0.2671% (0.733 ) 16-4 x=0

using Binomial calculator P(224)= 0.345954 P(x<4) ? 0.3460 so sebability of fewer then u do nut cover their mouth is 0.3460 P(x9). fewer than realf out of 16 cover mouth P(028) - x abc 도 0.733 )' (0.267)"6_2 (As hele = Coule calculator (P=0.733) Using Binomial monte PC*28) 0.0118 a 99 No Fewer than Half of 16 inclivi duel will be covering their mouth surprising because Probability of observing bewer than Half covering their when sneering is which unusual event . mouth 0.0118