Sneeze According to a study done by Nick Wilson of Otago University Wellington, 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 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

(b) What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth?

(c) Would you be surprised if, after observing 10 individuals, fewer than half covered their mouth when sneezing? Why?

Step 1 of 3

Given:

Sneeze According to a study done by Nick Wilson of Otago University Wellington, 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)

Let x be the number of person do not cover their mouth.

Let the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

P = 0.267

Let the sample size n = 10.

Let x follows binomial distribution with parameter np.

Here n = 10 and P = 0.267

The probability of a mass function of a binomial distribution is

P(X = x) = , for x = 0, 1, 2, . . . , n

Here we find the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing.

P(X = 4) =

P(X = 4) = 0.165534

P(X = 4) 0.1655

Therefore the probability exactly 4 do not cover their mouth when sneezing is 0.1655

In 100 trials of this experiment,we would expect about 2 trials to trials in exactly 4 do not cover their mouth when sneezing.