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 sit on a bench in a mall and observe people's habits as they sneeze. (a) what is the probability that among 18 randomly observed individuals exactly 8 do not cover their mouth when sneezing? (b) what is the probability that among 18 randomly observed individuals fewer than 6 do not cover their mouth when sneezing? (c) would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?
Accepted Solution
A:
Answer: kindly check explanation Step-by-step explanation:Probability of not covering mouth = p(success) = 0.267Hence, p(covering mouth) = 1 - 0.267 = 0.733a) What is the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing? Number of samples (n) = 12P(X = 8)Using binomial distribution :P(x) = nCx * p^x * (1-p)^(n-x)P(x =8) = 12C8 * 0.267^8 * 0.733^(12-8)P(x =8) = 12C8 * 0.267^8 * 0.733^4= 0.00369b) What is the probability that among 12 randomly observed individuals fewer than 6 do not cover their mouth when sneezing?P(X < 6) = p(5) + p(4) + p(3) + p(2) + p(1) + p(0)To save computation time, we can use an online binomial probability calculator :P(X < 6) = 0.9275C.) Yes, I will be surprised, because from the binomial probability obtained above, there is a high probability (0.9275) that fewer than half do not cover their mouth.