### Solution Found!

# Solved: Sneeze According to a study done by Nick Wilson of

**Chapter 11, Problem 39AYU**

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### Questions & Answers

**QUESTION:**

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?

**ANSWER:**

Step 1 of 4

Given:

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) = \(n C_{x} p^{x}(1-p)^{n-x}\) , for x = 0, 1, 2, . . . , n

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